Question

Can someone please factor this for me?

4x^2-12x+9 and give a step-by-step explanation? I really don't understand how to do this.

Answer 1

`\\ \rm\Rrightarrow 4x^2-12x+9`

`\\ \rm\Rrightarrow (2x)^2-2(2x)(3)+3^2`

So

• (a-b)²=a²-2ab+b²

`\\ \rm\Rrightarrow (2x-3)^2`

`\\ \rm\Rrightarrow (2x-3)(2x-3)`

Answer 2

`\left(2x-3\right)^2`

Explanation:

`4x^2-12x+9`

`\mathrm{Rewrite\:in\:the\:form\:of}\:a^2+2ab+b^2:`

`4x^2=(2x)^2`

`9=3^2`

`-12x=-2\cdot 2x\cdot 3`

`=\left(2x\right)^2-2\cdot \:2x\cdot \:3+3^2`

`\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \:a^2-2ab+b^2=\left(a-b\right)^2`

`\left(2x\right)^2-2\cdot \:2x\cdot \:3+3^2=\left(2x-3\right)^2`

`=\left(2x-3\right)^2`

~Learn with Lenvy~