## Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions)

**Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions)**

### Algebraic Expressions Exercise 11A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Separate the constants and variables from the following :

Solution:

Question 2.

Write the number of terms in each of the following polynomials.

(i) 5x^{2} + 3 x ax

(ii) ax ÷ 4 – 7

(iii) ax – by + y x z

(iv) 23 + a x b ÷ 2.

Solution:

Question 3.

Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :

Solution:

Question 4.

Write the degree of each polynomial given below :

Solution:

Question 5.

Write the coefficient of :

(i) ab in 7abx ,

(ii) 7a in 7abx ;

(iii) 5x^{2} in 5x^{2} – 5x ;

(iv) 8 in a^{2} – 8ax + a ;

(v) 4xy in x^{2} – 4xy + y^{2}.

Solution:

Question 6.

In \(\frac { 5 }{ 7 }\) xy^{2}z^{3}, write the coefficient of

Solution:

Question 7.

In each polynomial, given below, separate the like terms :

Solution:

### Algebraic Expressions Exercise 11B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Evaluate :

Solution:

Question 2.

Add :

Solution:

Question 3.

Find the total savings of a boy who saves ₹ (4x – 6y) ; ₹ (6x + 2y) ; ₹ (4y – x) and ₹ (y – 2x) for four consecutive weeks.

Solution:

Question 4.

Subtract :

Solution:

Question 5.

(i) Take away – 3x^{3} + 4x^{2} – 5x + 6 from 3x^{3} – 4x^{2} + 5x – 6

(ii) Take m^{2} + m + 4 from -m^{2} + 3m + 6 and the result from m^{2} + m + 1.

Solution:

Question 6.

Subtract the sum of 5y^{2} + y – 3 and y^{2} – 3y + 7 from 6y^{2} + y – 2.

Solution:

Question 7.

What must be added to x^{4} – x^{3} + x^{2} + x + 3 to obtain x^{4} + x^{2} – 1 ?

Solution:

Question 8.

(i) How much more than 2x^{2} + 4xy + 2y^{2} is 5x^{2} + 10xy – y^{2} ?

(ii) How much less 2a^{2} + 1 is than 3a^{2} – 6 ?

Solution:

Question 9.

If x = 6a + 86 + 9c ; y = 2b – 3a – 6c and z = c – b + 3a ; find

(i) x + y + z

(ii) x – y + z

(iii) 2x – y – 3z

(iv) 3y – 2z – 5x

Solution:

Question 10.

The sides of a triangle are x^{2} – 3xy + 8, 4x^{2} + 5xy – 3 and 6 – 3x^{2} + 4xy. Find its perimeter.

Solution:

Question 11.

The perimeter of a triangle is 8y^{2} – 9y + 4 and its two sides are 3y^{2} – 5y and 4y^{2} + 12. Find its third side.

Solution:

Question 12.

The two adjacent sides of a rectangle are 2x^{2} – 5xy + 3z^{2} and 4xy – x^{2} – z^{2}. Find its perimeter.

Solution:

Question 13.

What must be subtracted from 19x^{4} + 2x^{3} + 30x – 37 to get 8x^{4} + 22x^{3} – 7x – 60 ?

Solution:

Question 14.

How much smaller is 15x – 18y + 19z than 22x – 20y – 13z + 26 ?

Solution:

Question 15.

How much bigger is 15x^{2}y^{2} – 18xy^{2} – 10x^{2}y than -5x^{2} + 6x^{2}y – 7xy ?

Solution:

### Algebraic Expressions Exercise 11C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Multiply :

Solution:

Question 2.

Multiply :

Solution:

Question 3.

Simplify :

(i) (7x – 8) (3x + 2)

(ii) (px – q) (px + q)

(iii) (5a + 5b – c) (2b – 3c)

(iv) (4x – 5y) (5x – 4y)

(v) (3y + 4z) (3y – 4z) + (2y + 7z) (y + z)

Solution:

Question 4.

The adjacent sides of a rectangle are x^{2} – 4xy + 7y^{2} and x^{3} – 5xy^{2}. Find its area.

Solution:

Question 5.

The base and the altitude of a triangle are (3x – 4y) and (6x + 5y) respectively. Find its area.

Solution:

Question 6.

Multiply -4xy^{3} and 6x^{2}y and verify your result for x = 2 and y= 1.

Solution:

Question 7.

Find the value of (3x^{3}) x (-5xy^{2}) x (2x^{2}yz^{3}) for x = 1, y = 2 and z = 3.

Solution:

Question 8.

Evaluate (3x^{4}y^{2}) (2x^{2}y^{3}) for x = 1 and y = 2.

Solution:

Question 9.

Evaluate (x^{5}) × (3x^{2}) × (-2x) for x = 1.

Solution:

Question 10.

If x = 2 and y = 1; find the value of (-4x^{2}y^{3}) × (-5x^{2}y^{5}).

Solution:

Question 11.

Evaluate:

(i) (3x – 2)(x + 5) for x = 2.

(ii) (2x – 5y)(2x + 3y) for x = 2 and y = 3.

(iii) xz (x^{2} + y^{2}) for x = 2, y = 1 and z= 1.

Solution:

Question 12.

Evaluate:

(i) x(x – 5) + 2 for x = 1.

(ii) xy^{2}(x – 5y) + 1 for x = 2 and y = 1.

(iii) 2x(3x – 5) – 5(x – 2) – 18 for x = 2.

Solution:

Question 13.

Multiply and then verify :

-3x^{2}y^{2} and (x – 2y) for x = 1 and y = 2.

Solution:

Question 14.

Multiply:

(i) 2x^{2} – 4x + 5 by x^{2} + 3x – 7

(ii) (ab – 1)(3 – 2ab)

Solution:

Question 15.

Simplify : (5 – x)(6 – 5x)(2 -x).

Solution:

### Algebraic Expressions Exercise 11D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

Divide :

Solution:

Question 2.

Find the quotient and the remainder (if any) when :

Solution:

Question 3.

The area of a rectangle is x^{3} – 8x^{2} + 7 and one of its sides is x – 1. Find the length of the adjacent side.

Solution:

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Question 4.

The product of two numbers is 16x^{4} – 1. If one number is 2x – 1, find the other.

Solution:

Question 5.

Divide x^{6} – y^{6} by the product of x^{2} + xy + y^{2} and x – y.

Solution:

### Algebraic Expressions Exercise 11E – Selina Concise Mathematics Class 8 ICSE Solutions

Simplify :

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution: