Question

Binomial is a common factor, we factorise by writing the given expression as the product of this binomial and the quotient of the given expression by the binomial.

Please explain this.​

Answer 1

Answer:

Factorization of algebraic expressions when a binomial is a common factor: The expression is written as the product of binomial and the quotient obtained by dividing the given expression is by its binomial. Here, we observe that the binomial (3x + 1) is common to both the terms.

Answer 2

Answer:

1. Factorize the algebraic expressions:

(i) 5a(2x - 3y) + 2b(2x - 3y) 

Solution: 

5a(2x - 3y) + 2b(2x - 3y) 

Here, we observe that the binomial (2x – 3y) is common to both the terms.

= (2x - 3y)(5a + 2b)

(ii) 8(4x + 5y)2 - 12(4x + 5y)

Solution:

8(4x + 5y)2 - 12(4x + 5y)

= 2 ∙ 4(4x + 5y)(4x + 5y) – 3 ∙ 4(4x + 5y)

Here, we observe that the binomial 4(4x + 5y) is common to both the terms.

= 4(4x + 5y) ∙ [2(4x + 5y) -3]

= 4(4x + 5y)(8x + 10y - 3). 

 

2. Factorize the expression 5z(x – 2y) - 4x +8y

Solution:

5z(x – 2y) - 4x + 8y

Taking -4 as the common factor from -4x + 8y, we get

= 5z(x – 2y) – 4(x - 2y)

Here, we observe that the binomial (x – 2y) is common to both the terms.

= (x – 2y) (5z – 4)

3. Factorize (x – 3y)2 – 5x + 15y

Solution:

(x – 3y)2 – 5x + 15y

Taking – 5 common form – 5x + 15y, we get

= (x – 3y)2 – 5(x – 3y)

= (x – 3y) (x – 3y) - 5(x – 3y)

Here, we observe that the binomial (x – 3y) is common to both the terms.

= (x – 3y) [(x – 3y) – 5]                                                       

= (x – 3y) (x – 3y – 5

Step-by-step explanation:

eae given 5 brainliest answer