How do you factor $x^{2} + 16 x + 64$ $x^2+16x+64$ ?

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How do you factor $x^{2} + 16 x + 64$ $x^2+16x+64$ ?

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Answer 1 · 2018-03-26T11:00:00

${(x + 8)}^{2}$ $(x+8)^2$

Explanation:

$x^{2} + 16 x + 64 is a perfect square$ $x^2+16x+64" is a "color(blue)"perfect square"$

$that is {(x + a)}^{2} = x^{2} + 2 a x + a^{2}$ $"that is "(x+a)^2=x^2+2ax+a^2$

$compare the coefficients of the x-term$ $"compare the coefficients of the x-term"$

$\Rightarrow 2 a = 16 \Rightarrow a = 8$ $rArr2a=16rArra=8$

$\to x^{2} + 16 a + 64 = {(x + 8)}^{2}$ $rarrx^2+16a+64=(x+8)^2$

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How do you factor $x^{2} + 16 x + 64$ $x^2+16x+64$ ?

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