Question

Factorise 4x² + 9 – 12x – a² – b² + 2ab

Answer 1

Solution

$4x {}^{2} + 9 - 12x - {a}^{2} - {b}^{2} + 2ab \\ \\ = (4x {}^{2} - 12x + 9) - ( {a}^{2} + {b}^{2} - 2ab) \\ \\ = (2x - 3) {}^{2} - (a - b) {}^{2} \\ \\ = [(2x - 3) + (a - b)][(2x - 3) - (a - b)] \\ \\ = (2x - 3 + a - b)(2x - 3 - a + b)$

$\huge \fbox \red{Hope This Helps}$

Answer 2

From the given question the correct answer is:

the factor of  4x² + 9 – 12x – a² – b² + 2ab is (2x+3-a+b)(2x-3+a+b)

Given:

4x² + 9 – 12x – a² – b² + 2ab

To find:

we have to factorization

4x² + 9 – 12x – a² – b² + 2ab

Solution:

we will factorize the 4x² + 9 – 12x – a²– b² + 2ab

First, we will grouped the expression

 =(4x² + 9 – 12x) – (a²– b² + 2ab)

=(4x² – 12x+ 9 ) – (a²+ 2ab– b² )

we know that

(a-b)²=a²+2ab-b²

we can write the eqaution

=(2x-3)²-(a-b)²

we also know that,

a²-b²=(a-b)(a+b)

so,

[(2x-3)-(a-b)][(2x-3)+(a-b)]

simplify the expression

(2x+3-a+b)(2x-3+a+b)

Hence, the factor of  4x² + 9 – 12x – a² – b² + 2ab is (2x+3-a+b)(2x-3+a+b)