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ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) When an algebraic expression can be written as the product of two or more expressions then each of these expressions is called ……….. of the given expression.
(ii) The process of finding two or more expressions whose product is the given expression is called ………..
(iii) HCF of two or more monomials = (HCF of their ……….. coefficients) × (HCF of their literal coefficients)
(iv) HCB of literal coefficients = product of each common literal raised to the ……….. power.
(v) To factorise the trinomial of the form x² + px + q, we need to find two integers a and b such that a + b = ……….. and ab = ………..
(vi) To factorise the trinomial of the form ax² + bx + c, where a, b and c are integers, we split b into two parts such that ……….. of these parts is b and there is ……….. ac.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Factorisation is the reverse process of multiplication.
(ii) HCF of two or more polynomials (with integral coefficients) is the smallest common factor of the given polynomials.
(iii) HCF of 6x²y² and 8xy³ is 2xy².
(iv) Factorisation by grouping is possible only if the given polynomial contains an even number of terms.
(v) To factorise the trinomial of the form ax² + bx + c where, a, b, c are integers we want to find two integers A and B such that
A + B = ac and AB = b
(vi) Factors of 4x² – 12x + 9 are (2x – 3) (2x – 3).
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 14):
Question 3.
H.C.F. of 6abc, 24ab², 12a²b is
(a) 6ab
(b) 6ab²
(c) 6a²b
(d) 6abc
Solution:

Question 4.
Factors of 12a²b + 15ab² are
(a) 3a(4ab + 5b2)
(b) 3ab(4a + 5b)
(c) 3b(4a² + 5ab)
(d) none of these
Solution:

Question 5.
Factors of 6xy – 4y + 6 – 9x are
(a) (3y – 2) (2x – 3)
(b) (3x – 2) (2y – 3)
(c) (2y – 3) (2 – 3x)
(d) none of these
Solution:

Question 6.
Factors of 49p³q – 36pq are
(a) p(7p + 6q) (7p – 6q)
(b) q(7p – 6) (7p + 6)
(c) pq(7p + 6) (7p – 6)
(d) none of these
Solution:

Question 7.
Factors of y(y – z) + 9(z – y) are
(a) (y – z) (y + 9)
(b) (z – y) (y + 9)
(c) (y – z) (y – 9)
(d) none of these
Solution:

Question 8.
Factors of (lm + l) + m + 1 are
(a) (lm + l )(m + l)
(b) (lm + m)(l + 1)
(c) l(m + 1)
(d) (l + 1)(m + 1)
Solution:

Question 9.
Factors of z² – 4z – 12 are
(a) (z + 6)(z – 2)
(b) (z – 6)(z + 2)
(c) (z – 6)(z – 2)
(d) (z + 6)(z + 2)
Solution:

Question 10.
Factors of 63a² – 112b² are
(a) 63 (a – 2b)(a + 2b)
(b) 7(3a + 2b)(3a – 2b)
(c) 7(3a + 4b)(3a – 4b)
(d) none of these
Solution:

Question 11.
Factors of p⁴ – 81 are
(a) (p² – 9)(p² + 9)
(b) (p + 3)² (p – 3)²
(c) (p + 3) (p – 3) (p² + 9)
(d) none of these
Solution:

Question 12.
Factors of 3x + 7x – 6 are
(a) (3x – 2)(x + 3)
(b) (3x + 2) (x – 3)
(c) (3x – 2)(x – 3)
(d) (3x + 2) (x + 3)
Solution:

Question 13.
Factors of 16x² + 40x + 25 are
(a) (4x + 5)(4x + 5)
(b) (4x + 5)(4x – 5)
(c) (4x + 5)(4x + 8)
(d) none of these
Solution:

Question 14.
Factors of x² – 4xy + 4y² are
(a) (x – 2y)(x + 2y)
(b) (x-2y)(x-2y)
(c) (x + 2y)(x + 2y)
(d) none of these
Solution:

Higher Order Thinking Skills (Hots)
Factorise the following
Question 1.
x² + \(\left(a+\frac{1}{a}\right)\)x + 1
Solution:

Question 2.
36a⁴ – 97a²b² + 36b⁴
Solution:

Question 3.
2x² – \(\sqrt{3}\)x – 3
Solution:

Question 4.
y(y² – 2y) + 2(2y – y²) – 2 + y
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.5

Question 1.
Work out the following divisions:
(i) (35x + 28) ÷ (5x + 4)
(ii) 7p²q²(9r – 27) ÷ 63pq(r – 3)
Solution:

Question 2.
Divide as directed:
(i) 6(2x + 7) (5x – 3) ÷ 3(5x – 3)
(ii) 33pq (p + 3) (2q – 5) ÷ 11p (2q – 5)
Solution:

Question 3.
Factorise the expression and divide them as directed:
(i) (7x² – 63x) ÷ 7(x – 3)
(ii) (3p² + 17p + 10) ÷ (p + 5)
(iii) 10xy(14y² + 43y – 21) ÷ 5x(7y – 3)
(iv) 12pqr(6p² – 13pq + 6q²) ÷ 6pq(2p – 3q)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.4

Factorise the following (1 to 11) polynomials:
Question 1.
(i) x² + 3x + 2,
(ii) z² + 10z + 24
Solution:

Question 2.
(i) y² – 7y + 12
(ii) m² – 23m + 42
Solution:

Question 3.
(i) y² – 5y – 24,
(ii) t² + 23t – 108
Solution:

Question 4.
(i) 3x² + 14x + 8,
(ii) 3y² + 10y + 8
Solution:

Question 5.
(i) 14x² – 23x + 8,
(ii) 12x² – x – 35
Solution:

Question 6.
(i) 6x² + 11x – 10
(ii) 5 – 4x – 12x²
Solution:

Question 7.
(i) 1 – 18y – 63y²,
(ii) 3x² – 5xy – 12y²
Solution:

Question 8.
(i) x² – 3xy – 40y²
(ii) 10p²q² – 21pq + 9
Solution:

Question 9.
(i) 2a²b² + ab – 45
(ii) x (12x + 7) – 10
Solution:

Question 10.
(i) (a + b)² – 11(a + b) – 42
(ii) 8 + 6(p + q) – 5(p + q)
Solution:

Question 11.
(i) (x – 2y)² – 6(x – 2y) + 5
(ii) 7 + 10(2x – 3y) – 8(2x – 3y)²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.3

Question 1.
Factorise the following expressions using algebraic identities:
(i) x² – 12x + 36
(ii) 36p² – 60pq + 25q²
(iii) 9y² + 66xy + 121y²
(iv) a⁴ + 6a²b² + 9b⁴
(v) x² + \(\frac{1}{x^{2}}\) + 2
(vi) x² + x + \(\frac{1}{4}\)
Solution:

Factorise the following (2 to 13) expressions:
Question 2.
(i) 4p² – 9
(ii) 4x² – 169y²
Solution:

Question 3.
(i) 9x²y² – 25
(ii) 16x² – \(\frac{1}{144}\)
Solution:

Question 4.
(i) 20x² – 45y²
(ii) \(\frac{9}{16}\) – 25a²b²
Solution:

Question 5.
(i) (2a + 3b)² – 16c²
(ii) 1 – (b – c)²
Solution:

Question 6.
(i) 9 (x + y)² – x²
(ii) (2m + 3n)² – (3m + 2n)²
Solution:

Question 7.
(i) 25 (a + b)² – 16 (a – b)²
(ii) 9 (3x + 2)² – 4 (2x – 1)²
Solution:

Question 8.
(i) x³ – 25x
(ii) 63p²q² – 7
Solution:

Question 9.
(i) 32a²b – 72b³
(ii) 9 (a + b)³ – 25 (a + b)
Solution:

Question 10.
(i) x² – y² – 2y – 1
(ii) p²– 4pq + 4q² – r²
Solution:

Question 11.
(i) 9x² – y² + 4y – 4
(ii) 4a² – 4b² + 4a + 1
Solution:

Question 12.
(i) 625 – p⁴
(ii) 5y⁵ – 405y
Solution:

Question 13.
(i) x⁴ – y⁴ + x² – y²
(ii) 64a² – 9b² + 42bc – 49c²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.2

Factorise the following (1 to 11) polynomials:
Question 1.
(i) x² + xy – x – y
(ii) y² – yz – 5y + 5z
Solution:

Question 2.
(i) 5xy + 7y – 5y² – 7x
(ii) 5p² – 8pq – 10p + 16q
Solution:

Question 3.
(i) a²b – ab² + 3a – 3b
(ii) x³ – 3x² + x – 3
Solution:

Question 4.
(i) 6xy² – 3xy – 10y + 5
(ii) 3ax – 6ay – 8by + 4bx
Solution:

Question 5.
(i) x² + xy (1 + y) + y³
(ii) y² – xy (1 – x) – x³
Solution:

Question 6.
(i) ab² + (a – 1) b – 1
(ii) 2a – 4b – xa + 2bx
Solution:

Question 7.
(i) 5ph – 10qk + 2rph – 4qrk
(ii) x² – x(a + 2b) + 2a²
Solution:

Question 8.
(i) ab (x² + y²) – xy (a² + b²)
(ii) (ax + by)² + (bx – ay)²
Solution:

Question 9.
(i) a³ + ab(1 – 2a) – 2b²
(ii) 3x²y – 3xy + 12x – 12
Solution:

Question 10.
(i) a²b + ab² – abc – b²c + axy + bxy
(ii) ax² – bx² + ay² – by² + az² – bz²
Solution:

Question 11.
(i) x – 1 – (x – 1)² + ax – a
(ii) ax + a²x + aby + by – (ax + by)²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.1

Factorise the following (1 to 8) polynomials:
Question 1.
(i) 8xy³ + 12x²y²
(ii) 15ax³ – 9ax²
Solution:

Question 2.
(i) 21 py² – 56py
(ii) 4x³ – 6x²
Solution:

Question 3.
(i) 25abc² – 15a²b²c
(ii) x²yz + xy²z + xyz²
Solution:

Question 4.
(i) 8x³ – 6x² + 10x
(ii) 14mn + 22m – 62p
Solution:

Question 5.
(i) 18p²q² – 24pq² + 30p²q
(ii) 27a³b³ – 18a²b³ + 75a³b²
Solution:

Question 6.
(i) 15a (2p – 3p) – 106 (2p – 3q)
(ii) 3a (x² + y²) + 6b (x² + y²)
Solution:

Question 7.
(i) 6(x + 2y)³ + 8(x + 2y)²
(ii) 14(a – 3b)³ – 21p(a – 3b)
Solution:

Question 8.
10a (2p + q)³ – 15b (2p + q)² + 35(2p + q)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Check Your Progress

Question 1.
Add the following expressions:
(i) -5x²y + 3xy² – 7xy + 8, 12x²y – 5xy² + 3xy – 2
(ii) 9xy + 3yz – 5zx, 4yz + 9zx – 5y, -5xz + 2x – 5xy
Solution:

Question 2.
Subtract:
(i) 5a + 3b + 11c – 2 from 3a + 5b – 9c + 3
(ii) 10x² – 8y² + 5y – 3 from 8x² – 5xy + 2y² + 5x – 3y
Solution:

Question 3.
What must be added to 5x² – 3x + 1 to get 3x³ – 7x² + 8?
Solution:

Question 4.
Find the product of
(i) 3x²y and -4xy²
(ii) –\(\frac{4}{5}\)xy, \(\frac{5}{7}\)yz and –\(\frac{14}{9}\)zx
Solution:

Question 5.
Multiply:
(i) (3pq – 4p² + 5q² + 7) by -7pq
(ii) (\(\frac{3}{4}\)x²y – \(\frac{4}{5}\)xy + \(\frac{5}{6}\)xy²) by – 15xyz
Solution:

Question 6.
Multiply:
(i) (5x² + 4x – 2) by (3 – x – 4x²)
(ii) (7x² + 12xy – 9y²) by (3x² – 5xy + 3y²)
Solution:

Question 7.
Simplify the following expressions and evaluate them as directed:
(i) (3ab – 2a² + 5b²) x (2b² – 5ab + 3a²) + 8a³b – 7b⁴ for a = 1, b = -1
(ii) (1.7x – 2.5y) (2y + 3x + 4) – 7.8x² – 10y for x = 0, y = 1.
Solution:

Question 8.
Carry out the following divisions:
(i) 66pq²r³ ÷ 11qr²
(ii) (x³ + 2x² + 3x) ÷ 2x
Solution:

Question 9.
Divide 10x⁴ – 19x³ + 17x² + 15x – 42 by 2x² – 3x + 5.
Solution:

Question 10.
Using identities, find the following products:
(i) (3x + 4y) (3x + 4y)
(ii) \(\left(\frac{5}{2} a-b\right)\left(\frac{5}{2} a-b\right)\)
(iii) (3.5m – 1.5n) (3.5m + 1.5n)
(iv) (7xy – 2)(7xy + 7)
Solution:

Question 11.
Using suitable identities, evaluate the following:
(i) 105²
(ii) 97²
(iii) 201 × 199
(iv) 87² – 13²
(v) 105 × 107
Solution:

Question 12.
Prove that following:
(i) (a + b)² – (a – b)² + 4ab
(ii) (2a + 3b)² + (2a – 3b)² = 8a² + 18b²
Solution:

Question 13.
If x + \(\frac{1}{x}\) = 5, evaluate

Solution:

Question 14.
If a + b = 5 and a² + b² = 13, find ab.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A symbol which has a fixed value is called a ……….
(ii) A symbol which can be given various numerical values is called ……….. or ………
(iii) The various parts of an algebraic expression separated by + or – sign are called ………..
(iv) An algebraic expression having ………… terms is called a binomial.
(v) Each of the quantity (constant or literal) multiplied together to form a product is called a ………… of the product.
(vi) The terms having the same literal coefficients are called a ………… otherwise they are called …………
(vii) Degree of the polynomial is the greatest sum of the powers of ………… in each term.
(viii)An identity is equality which is true for ………… of variables in it.
(ix) (a + b)² = …………
(x) (x + a) (x + b) = x² + ………… + ab.
(xi) Dividend = ………… + remainder.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) An algebraic expression having only one term is called a monomial.
(ii) A symbol which has fixed value is called a literal.
(iii) The term of an algebraic expression having no literal factor is called its constant term,
(iv) In any term of an algebraic expression the constant part is called literal coefficient of the term.
(v) An algebraic expression is called polynomial if the powers of the variables involved in it in each term are non-negative integers.
(vi) 5x²y²z, 3x²zy², – \(\frac{4}{5}\) zx²y² are unlike terms.
(vii) 5x + \(\frac{2}{x}\) + 7 is a polynomial of degree 1.
(viii) 3x²y + 7x + 8y + 9 is a polynomial of degree 3.
(ix) Numerical coefficient of -7x³y is 7.
(x) An equation is true for all values of variables in it.
(xi) (a – b)² + 2ab = a² + b².
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 18):
Question 3.
The literal coefficient of -9xyz² is
(a) -9
(b) xy
(c) xyz²
(d) -9xy
Solution:

Question 4.
Which of the following algebraic expression is
(a) 3x² – 2x + 7
(b) \(\frac{5 x^{3}}{2 x}\) + 3x² + 8
(c) 3x + \(\frac{2}{x}\) + 7
(d) \(\sqrt{2}\)x² + \(\sqrt{3}\)x + \(\sqrt{6}\)
Solution:

Question 5.
Which of the following algebraic expressions is not a monomial?
(a) 3x × y × z
(b) -5pq
(c) 8m² × n ÷ 31
(d) 7x ÷ y – z
Solution:

Question 6.
Degree of the polynomial 7x²yz² + 6x³y²z² – 5x + 8y is
(a) 4
(b) 5
(c) 6
(d) 7
Solution:

Question 7.
a(b -c) + b(c – a) + c(a – b) is equal to
(a) ab + bc + ca
(b) 0
(c) 2(ab + bc + ca)
(d) none of these
Solution:

Question 8.
\(\frac{7}{5}\)xy – \(\frac{2}{3}\)xy + \(\frac{8}{9}\) xy is equal to

Solution:

Question 9.
(3p²qr³) × (-4p³q²r²) x (7pq³r) is equal to
(a) 84p⁶q⁶r⁶
(b) -84p⁶q⁶r⁶
(c) 84p⁶q⁵r⁶
(d) -84p⁶q⁵r⁶
Solution:

Question 10.
3m × (2m² – 5mn + 4n²) is equal to
(a) 6m³ + 15m²n – 12mn²
(b) 6m³ – 15m²n + 12mn²
(c) 6m³ – 15m²n – 12mn²
(d) 6m³ + 15m²n + 12mn²
Solution:

Question 11.
Volume of a rectangular box whose adjacent edges are 3x²y, 4y²z and 5z²x respectively is
(a) 60xyz
(b) 60x²y²z²
(c) 60x³y³z³
(d) none of these
Solution:

Question 12.
(x – 1) (x + 2) is equal to
(a) 2x + 3
(b) x² + 2x + 2
(c) x² + 3x + 2
(d) x² + 2x + 3
Solution:

Question 13.
If x + \(\frac{1}{x}\) = 2, then x² + \(\frac{1}{x^{2}}\) is equal to
(a) 4
(b) 2
(c) 0
(d) none of these
Solution:

Question 14.
If x² + y² = 9 and xy = 8, then x + y is equal to
(a) 25
(b) 5
(c) -5
(d) ±5
Solution:

Question 15.
(102)² – (98)² is equal to
(a) 200
(b) 400
(c) 600
(d) 800
Solution:

Question 16.
-50x³y²z² divided by -5xyz is equal to
(a) 10xyz
(b) 10x²yz
(c) -10xyz
(d) -10x²yz
Solution:

Question 17.
96 × 104 is equal to
(a) 9984
(b) 9974
(c) 9964
(d) none of these
Solution:

Question 18.
If the area of a rectangle is 24(x²yz + xy²z + xyz²) and its length is 8xyz, then its breadth is
(a) 3(x + y + z)
(b) 3xyz
(c) 3(x + y – z)
(d) none of these
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
Using the identity (a + b) = a² + 2ab + b², derive the formula for (a + b + c)². Hence, find the value of (2x – 3y + 4z)².
Solution:

Question 2.
Using the product of algebraic expressions, find the formulas for (a + b)² and (a – b).
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.5

Question 1.
Using suitable identities, find the following products:
(i) (3x + 5) (3x + 5)
(ii) (9y – 5) (9y-5)
(iii) (4x + 11y) (4x – 11y)
(iv) \(\left(\frac{3}{2} m+\frac{2}{3} n\right)\left(\frac{3}{2} m-\frac{2}{3} n\right)\)
(v) \(\left(\frac{2}{a}+\frac{5}{b}\right)\left(\frac{2}{a}+\frac{5}{b}\right)\)
(vi) \(\left(\frac{p^{2}}{2}+\frac{2}{q^{2}}\right)\left(\frac{p^{2}}{2}-\frac{2}{q^{2}}\right)\)
Solution:

Question 2.
Using the identities, evaluate the following:
(i) 81²
(ii) 97²
(iii) 105²
(iv) 997²
(v) 6.1²
(vi) 496 × 504
(vii) 20.5 × 19.5
(viii) 9.62
Solution:

Question 3.
Find the following squares, using the identities:

Solution:

Question 4.
Using the identity, (x + a) (x + b) = x² + (a + b)x + ab, find the following products:
(i) (x + 7) (x + 3)
(ii) (3x + 4) (3x – 5)
(iii) (p² + 2q) (p² – 3q)
(iv) (abc + 3) (abc – 5)
Solution:

Question 5.
Using the identity, (x + a) (x + b) = x² + (a + b)x + ab, evaluate the following:
(i) 203 × 204
(ii) 8.2 × 8.7
(iii) 107 × 93
Solution:

Question 6.
Using the identity a² – b² = (a + b) (a – b), find
(i) 53² – 47²
(ii) (2.05)² – (0.95)²
(iii) (14.3)² – (5.7)²
Solution:

Question 7.
Simplify the following:
(i) (2x + 5y)² + (2x – 5y)²
(ii) \(\left(\frac{7}{2} a-\frac{5}{2} b\right)^{2}-\left(\frac{5}{2} a-\frac{7}{2} b\right)^{2}\)
(iii) (p² – q²r)² + 2p²q²r
Solution:

Question 8.
Show that:
(i) (4x + 7y)² – (4x – 7y)² = 112xy
(ii) \(\left(\frac{3}{7} p-\frac{7}{6} q\right)^{2}+p q=\frac{9}{49} p^{2}+\frac{49}{36} q^{2}\)
(iii) (p – q)(p + q) + (q – r)(q + r) + (r – p) (r + p) = 0
Solution:

Question 9.
If x + \(\frac{1}{x}\) = 2, evaluate:

Solution:

Question 10.
If x = \(\frac{1}{x}\) = 7, ecaluate:

Solution:

Question 11.
If x² + \(\frac{1}{x^{2}}\) = 23, evaluate:

Solution:

Question 12.
If a + b = 9 and = 10, find the value of a² + b².
Solution:

Question 13.
If a – b = 6 and a² + b² = 42, find the value of
Solution:

Question 14.
If a² + b² = 41 and ab = 4, find the values of
(i) a + b
(ii) a – b
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.4

Question 1.
Divide:
(i) – 39pq²r⁵ by – 24p³q³r
(ii) –\(\frac{3}{4}\)a²b³ by \(\frac{6}{7}\)a³b²
Solution:

Question 2.
Divide:
(i) 9x⁴ – 8x³ – 12x + 3 by 3x
(ii) 14p²q³ – 32p³q² + 15pq² – 22p + 18q by – 2p²q.
Solution:

Question 3.
Divide:
(i) 6x² + 13x + 5 by 2x + 1
(ii) 1 + y³ by 1 + y
(iii) 5 + x – 2x² by x + 1
(iv) x³ – 6x² + 12x – 8 by x – 2
Solution:

Question 4.
Divide:
(i) 6x³ + x² – 26x – 25 by 3x – 7
(ii) m³ – 6m² + 7 by m – 1
Solution:

Question 5.
Divide:
(i) a³ + 2a² + 2a + 1 by + a² + a + 1
(ii) 12x³ – 17x² + 26x – 18 by 3x² – 2x + 5
Solution:

Question 6.
If the area of a rectangle is 8x² – 45y² + 18xy and one of its sides is 4x + 15y, find the length of the adjacent side.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.3

Question 1.
Multiply:
(i) (5x – 2) by (3x + 4)
(ii) (ax + b) by (cx + d)
(iii) (4p – 7) by (2 – 3p)
(iv) (2x² + 3) by (3x – 5)
(v) (1.5a – 2.5b) by (1.5a + 2.56)
(vi) \(\left(\frac{3}{7} p^{2}+4 q^{2}\right) \text { by } 7\left(p^{2}-\frac{3}{4} q^{2}\right)\)
Solution:

Question 2.
Multiply:
(i) (x – 2y + 3) by (x + 2y)
(ii) (3 – 5x + 2 × 2) by (4x – 5)
Solution:

Question 3.
Multiply:
(i) (3x² – 2x – 1) by (2x² + x – 5)
(ii) (2 – 3y – 5y²) by (2y – 1 + 3y²)
Solution:

Question 4.
Simplify:
(i) (x² + 3) (x – 3) + 9
(ii) (x + 3) (x – 3) (x + 4) (x – 4)
(iii) (x + 5) (x + 6) (x + 7)
(iv) (p + q – 2r) (2p – q + r) – 4qr
(v) (p + q) (r + s) + (p – q)(r – s) – 2(pr + qs)
(vi) (x + y + z) (x – y + z) + (x + y – z) (-x + y + z) – 4zx
Solution:

Question 5.
If two adjacent sides of a rectangle are 5x² + 25xy + 4y² and 2x² – 2xy + 3y², find its area.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths