Question

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

16x240x+2516 x^2-40 x+25

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}

16x240x+25=(4x)2a22(4x)(5)2ab+52b2=(4x5)2\begin{aligned} 16x^2& - 40x + 25\\ &=\underbrace{(4x)^2}_{a^2}-\underbrace{2\cdot(4x)\cdot(5)}_{2ab}+\underbrace{5^2}_{b^2}\\ &=(4x-5)^2 \end{aligned}

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