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 · 2017-02-17T00:12:05

$x^{2} + 16 x + 64 = {(x + 8)}^{2}$ $x^2+16x+64 = (x+8)^2$ is a perfect square trinomial.

Explanation:

Given:

$x^{2} + 16 x + 64$ $x^2+16x+64$

Note that both $x^{2}$ $x^2$ and $64 = 8^{2}$ $64=8^2$ are both perfect squares, so we should check whether the middle term matches the middle term of ${(x + 8)}^{2}$ $(x+8)^2$ ...

${(x + 8)}^{2} = x^{2} + 2 (x) (8) + 8^{2} = x^{2} + 16 x + 64$ $(x+8)^2 = x^2+2(x)(8)+8^2 = x^2+16x+64$

So $x^{2} + 16 x + 64 = {(x + 8)}^{2}$ $x^2+16x+64 = (x+8)^2$ is a perfect square trinomial.

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

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