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Question

Factor each perfect square trinomial. It may be necessary to factor out a common factor first.

9x212x+49 x^2-12 x+4

Solution

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Answered 2 years ago
Answered 2 years ago
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Let's factor the perfect square trinomial.

(a±b)2=a2±2ab+b2\begin{aligned}(a\pm b)^2 = a^2\pm2ab+b^2\end{aligned}

9x212x+4=(3x)2a22(3x)(2)2ab+22b2=(3x2)2\begin{aligned} 9x^2& - 12x + 4\\ &=\underbrace{(3x)^2}_{a^2}-\underbrace{2\cdot(3x)\cdot(2)}_{2ab}+\underbrace{2^2}_{b^2}\\ &=(3x-2)^2 \end{aligned}

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