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

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