146k views
10 votes
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.

User Vretamal
by
6.7k points

2 Answers

11 votes


\\ \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)

User Vivek Srinivasan
by
6.9k points
7 votes

Answer:


\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~

User Taylour
by
6.1k points
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