Chapter 6: Algebraic Expressions and Identities Exercise – 6.5

Question: 1

Multiply

(5x + 3) by (7x + 2)

Solution:

To multiply, we will use distributive law as follows:

(5x + 3)(7x + 2)

= 5x(7x + 2)+ 3(7x + 2)

= (5x × 7x + 5x × 2) + (3 × 7x + 3 × 2)

= (35 x 2 + 10x) + (21x + 6)

= 35x² + 10x + 21x + 6

= 35x² + 31x + 6

Thus, the answer is 35x² + 31x + 6

 

Question: 2

Multiply

(2x + 8) by (x – 3)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 3

Multiply

(7x + y) by (x + 5y)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 4

Multiply

(a – 1) by (0.1a² + 3)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 5

Multiply

(3x² + y²) (2x² + 3y²)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 6

Multiply

Solution:

To multiply, we will use distributive law as follows:

 

Question: 7

Multiply

(x⁶ - y⁶)(x² + y²)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 8

Multiply

(x² + y²) (3a + 2b)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 9

Multiply

[ – 3d + (–7f)](5d + f)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 10

Multiply

(0.8a – 0.5b)(1.5a – 3b)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 11

Multiply

(2x²y² – 5xy²)(x² – y²)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 12

Multiply

Solution:

To multiply, we will use distributive law as follows:

 

Question: 13

Multiply

Solution:

To multiply, we will use distributive law as follows:

 

Question: 14

Multiply

(3x²y – 5xy²)((1/5)x² + (1/3)y²)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 16

Multiply

(2xy + 3y²)(3y² – 2)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 17

Find the products and verify the result for x = -1 and y = -2:

(3x – 5y)(x + y)

Solution:

 

Question: 18

Find the products and verify the result for x = -1 and y = – 2:

(x²y – 1)(3 – 2x²y)

Solution:

To multiply, we will use distributive law as follows:

 

Question: 19

Find the products and verify the result for x = -1 and y = -2:

Solution:

To multiply, we will use distributive law as follows:

 

Question: 20

Simplify

x²(x + 2y)(x – 3y)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 21

Simplify

(x² – 2y²)(x + 4y) x²y²

Solution:

To simplify, we will use distributive law as follows:

 

Question: 22

Simplify

a²b²(a + 2b)(3a + b)

Solution:

To simplify, we will use distributive law as follows: 

 

Question: 23

Simplify

x²(x – y)y²(x + 2y)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 24

Simplify

(x³ – 2x² + 5x – 7)(2x – 3)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 25

Simplify

2x⁴ – 7x³ + 16x ²– 29x + 21

Solution:

To simplify, we will use distributive law as follows:

 

Question: 26

Simplify

(5 – x)(6 – 5x)(2– x)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 27

Simplify

(2x² + 3x – 5)(3x² – 5x + 4)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 28

Simplify

(3x – 2)(2x – 3) + (5x – 3)(x + 1)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 29

Simplify

(5x – 3)(x + 2) – (2x + 5)(4x – 3)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 30

Simplify

(3x + 2y)(4x + 3y) – (2x – y)(7x – 3y)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 31

Simplify

(x² – 3x + 2)(5x – 2) – (3x² + 4x – 5)(2x – 1)

Solution:

To simplify, we will use distributive law as follows:

 

Question: 32

Simplify

(x³ – 2x² + 3x – 4)(x – 1) – (2x – 3)(x² – x + 1)

Solution:

To simplify, we will use distributive law as follows: