Question

Factorize:
9(2a - b)² - 4(2a - b) -13

Answer 1

Concept :  

Here we factorise it by splitting the middle term.

To factorise quadratic polynomials of the type ax² + bx + c by middle term splitting ,write b as the sum of two numbers whose product is ac.

To factorise ax² + bx - c & ax²- bx - c , write b as the difference of two numbers whose product is - ac.

 

Given :  9(2a - b)² - 4(2a - b) -13

Let (2a – b) = x  

Now we can write the given expression as ;  

= 9x² - 4x - 13

= 9x² - 13x + 9x - 13

[By middle term splitting]

= x(9x - 13) + 1 (9x - 13)

= (9x - 13) (x + 1)………….(1)

On putting x = (2a – b) in  eq 1:  

= [9(2a – b) – 13] [2a – b + 1]

= (18a – 9b – 13) (2a – b + 1)

Hence, the factorisation of 9(2a - b)² - 4(2a - b) -13 is (18a – 9b – 13) (2a – b + 1).

HOPE THIS ANSWER WILL HELP YOU…..

 

Some questions of this chapter :

Factorize:

7(x-2y)²-25(x-2y)+12

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Factorize:

X²+6√2x+10

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Answer 2

9(2a - b)² - 4(2a - b) -13

=(2a - b) {9(2a - b)²-4-13}

=(2a - b) {9(4a^2-4ab+b^2)-4-13}

=(2a - b) (36a^2-36ab+9b^2-4-13)