Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 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:
Clearly constants are : -7, √5, 8 – 5
 
Question 2.
Write the number of terms in each of the following polynomials.
(i) 5x2 + 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:
(i) degree = 2 (Polynomial is xy + 7z)
(ii) degree = 3 (Polynomial is x2 – 6x3 + 8 y)
(iii) degree = 8 (Polynomial is y – 6y2 + 5y8)
(iv) degree = 3 (Polynomial is xyz – 3)
(v) degree = 4 (Polynomial is xy + yz2 – xz3)
(vi) degree = 12 (Polynomial is x5y7 – 8x3y8 + 10x4, y4z4)

Question 5.
Write the coefficient of :
(i) ab in 7abx ,
(ii) 7a in 7abx ;
(iii) 5x2 in 5x2 – 5x ;
(iv) 8 in a2 – 8ax + a ;
(v) 4xy in x2 – 4xy + y2.
Solution:
(i) The coefficient of ab in 7abx = 7x
(ii) The coefficient of 7a in 7abx = bx
(iii) The coefficient of 5x2 in 5x2 – 5x = 1
(iv) The coefficient of 8 in a2 – 8ax + a = – ax
(v) The coefficient of 4xy in x2 – 4xy + y2 = -1
Question 6.
In   xy2z3, 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 – 3x3 + 4x2 – 5x+ 6 from 3x3 – 4x2 + 5x – 6
(ii) Take m2 + m + 4 from -m2 + 3m + 6 and the result from m2 + m + 1.
Solution:
 
Question 6.
Subtract the sum of 5y2 + y – 3 and y2 – 3y + 7 from 6y2 + y – 2.
Solution:
 
Question 7.
What must be added to x4 – x3 + x2 + x + 3 to obtain x4 + x2 – 1 ?
Solution:
 
Question 8.
(i) How much more than 2x2 + 4xy + 2y2 is 5x2 + 10xy – y2 ?
(ii) How much less 2a2 + 1 is than 3a2 – 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 x2 – 3xy + 8, 4x2 + 5xy – 3 and 6 – 3x2 + 4xy. Find its perimeter.

Solution:

 
Question 11.

The perimeter of a triangle is 8y2 – 9y + 4 and its two sides are 3y2 – 5y and 4y2 + 12. Find its third side.

Solution:

 
Question 12.

The two adjacent sides of a rectangle are 2x2 – 5xy + 3z2 and 4xy – x2 – z2. Find its perimeter.

Solution:

 
Question 13.

What must be subtracted from 19x4 + 2x3 + 30x – 37 to get 8x4 + 22x3 – 7x – 60 ?

Solution:

 
 
Question 14.
How much smaller is 15x – 18y + 19z than 22x – 20y – 13z + 26 ?
Solution:
The required result is
(22x – 20y – 13z + 26) – (15x – 18y + 19z)
= 22x – 20y – 13z + 26 – 15x + 18y – 19z
= 7x – 2y – 32z + 26
Question 15.
How much bigger is 15x2y2 – 18xy2 – 10x2y than -5x2 + 6x2y – 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 x2 – 4xy + 7y2 and x3 – 5xy2. 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:

Reqd. Area =   (base) x (altitude)
 
Question 6.
Multiply -4xy3 and 6x2y and verify your result for x = 2 and y= 1.
Solution:
 
Question 7.
Find the value of (3x3) x (-5xy2) x (2x2yz3) for x = 1, y = 2 and z = 3.
Solution:
 
Question 8.
Evaluate (3x4y2) (2x2y3) for x = 1 and y = 2.
Solution:
 
Question 9.
Evaluate (x5) x (3x2) x (-2x) for x = 1.
Solution:
 
Question 10.
If x = 2 and y = 1; find the value of (-4x2y3) x (-5x2y5).
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 (x2 + y2) for x = 2, y = 1 and z= 1.
Solution:
 
Question 12.
Evaluate:
(i) x(x – 5) + 2 for x = 1.
(ii) xy2(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 :
-3x2y2 and (x – 2y) for x = 1 and y = 2.
Solution:
 
Question 14.
Multiply:
(i) 2x2 – 4x + 5 by x2 + 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 x3 – 8x2 + 7 and one of its sides is x – 1. Find the length of the adjacent side.

Solution:

 
Question 4.
The product of two numbers-is 16x4 – 1. If one number is 2x – 1, find the other.
Solution:
 
Question 5.
Divide x6 – y6 by the product of x2 + xy + y2 and x – y.
Solution:
 
Simplification
(Using removal of brackets)
The signs for different types of brackets are :
1. ____ ; Vinculum or bar brackets,
2. ( ); Parenthesis or small brackets,
3. { }; Curly brackets or middle brackets,
4. [ ]; Square brackets or big brackets.

In a combined operation, the brackets must be removed in the same order as written above:

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: