Question

this is a question of factorisation 8(4x+5y)²-12(4x+5y) but the answer is 4(4x+5y). (2(4x+5y)-3) how???? can u help pls​

Answer 1

$\large\underline{\sf{Solution-}}$

Given algebraic expression is

$\rm :\longmapsto\:8 {(4x + 5y)}^{2} - 12(4x + 5y)$

in factorized form can be rewritten as

$\rm \:  =  \: 2.2.2(4x + 5y)(4x + 5y) - 2.2.3(4x + 5y)$

$\rm \:  =  \: \red{2.2}.2 \red{(4x + 5y)}(4x + 5y) - \red{2.2}.3 \red{(4x + 5y)}$

$\rm \:  =  \: 2.2(4x + 5y)[2(4x + 5y) - 3]$

$\rm \:  =  \: 4(4x + 5y)[2(4x + 5y) - 3]$

Hence,

$\rm :\longmapsto\:8 {(4x + 5y)}^{2} - 12(4x + 5y) \\ \\ \rm \:  =  \: 4(4x + 5y)[2(4x + 5y) - 3]$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Concept Used :-

1. Method of Common Factors

Step :- 1 In this method, we have to first break down the terms in to the lowest factors.

Step :- 2 Now take out the respective common factors from all the terms.

Step :- 3 The product of the factors is the required factorization of the expression.

LEARN MORE

1. Factorisation by Regrouping Terms

Sometimes it is not possible to take out the common factors from all the terms. In such cases, we have to make the rearrangement of the terms in the groups to take out the common factors.

Find the common factor from these terms and it will give the required factors of the given expression.