Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions

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)

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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 \(\frac { 5 }{ 7 }\) 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 = \(\frac { 1 }{ 2 }\) (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: