Question

(2 x- 3)² - 8 x + 12 factorize it

Answer 1

(2x-3)² -8x+12=4x²+9-12x-8x+12
=4x²-20x+21=4x² -6x -14x+21
=2x(2x-3) -7(2x-3)
=(2x -7)(2x-3)

Answer 2

The factors of the given expression are $(2x-3)(2x-7)$ .

Step-by-step explanation:

We are given the following expression (2 x- 3)² - 8 x + 12 to factorize.

⇒  (2 x - 3)² - 8 x + 12

⇒  $(2x)^{2} + (3)^{2} - 2 (2x)(3) -8x+12$     {∵ $(a-b)^{2} = a^{2} +b^{2} -2ab$ }

⇒  $4x^{2} + 9 - 12x -8x+12$

⇒  $4x^{2} - 20x+21$

Now, we will use the method of Middle Term Splitting to factorize the above expression;

⇒  $4x^{2} - 14x - 6x+21$

⇒  $2x(2x-7) - 3(2x-7)$    {Taking 2x common from first two terms and -3

                                               common from next two terms}

⇒  $(2x-3)(2x-7)$

Hence, the factors of the given expression are $(2x-3)(2x-7)$ .