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

Answer:

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

Step-by-step 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~

Answer 2

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

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

So

• (a-b)²=a²-2ab+b²

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

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