How do you factor a perfect square trinomial $36b^2 − 24b + 16$ ?

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Answer 1 · 2015-06-12T14:00:51

We know that $(color(blue)a-color(red)b)²=color(blue)(a^2)-2color(blue)acolor(red)b+color(red)(b²)$

$36b^2=color(blue)((6b)²)=color(blue)(a^2)$ ( $color(blue)(a=6b$ )
$16=color(red)(4^2)=color(red)(b^2)$ ( $color(red)(b=4$ )

We are going to check if $-2ab=-24b$ :
$-2ab=-2*6b*4=-48b$ : incorrect

Thus $36b^2-24b+16$ is not a perfect square.

How do you factor a perfect square trinomial 36b^2 − 24b + 1636b^2 − 24b + 16?