Question

factorise 2x - 3 to the power square - 8 x + 12

Answer 1

Given that: (2x-3)^2-8x+12

So (2x-3)^2 = (2x-3)(2x-3)= 4x^2-6x-6x+9= 4x^2-12x+9

So (2x-3)^3-8x+12 = 4x^2-12x+9-8x-+12= 4x^2-20x+21

Using ac method: we need to find the pair factors of 84 which add upto -20

So -14*-6= 84 and -14-6 = -20

So 4x^2-20x+21= 4x^2-14x-6x+21 = 2x(2x-7)-3(2x-7)= (2x-7)(2x-3)

So (2x-3)^2-8x+12 = (2x-7)(2x-3)

Answer 2

Given,

(2x -3)² -8x +12

Expanding First term using identity:-

(a - b)² = a² + b² - 2ab

We get,

→(2x)² +3² -2*(2x)(3) -8x +12

→4x² + 9 -12x - 8x + 12

→4x² - 20x + 21

→4x² - 14x - 6x +21

→2x(2x -7) - 3(2x - 7)

→(2x- 3) ( 2x-7)