# Factor each polynomial. x^{2}-8x+16-y^{2}

Factor each polynomial.
${x}^{2}-8x+16-{y}^{2}$
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Annie Gonzalez
Step 1
We need to factor the following polynomial
${x}^{2}-8x+16-{y}^{2}$
Step 2
The polynomial can be factored as following
${x}^{2}-8x+16-{y}^{2}=\left({x}^{2}-8x+16\right)-{y}^{2}$
$={\left(x-4\right)}^{2}-{y}^{2}$
=[(x-4)-y][(x-4)+y] Using formula ${a}^{2}-{b}^{2}=\left(a-b\right)\left(a+b\right)$
=(x-4-y)(x-4+y)
Hence,
${x}^{2}-8x+16-{y}^{2}=\left(x-4-y\right)\left(x-4+y\right)$

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Dabanka4v
Step 1
To find the factor of the given polynomial.
Step 2
Given information:
${x}^{2}-8x+16-{y}^{2}$
Step 3
Calculation:
Rewrite (8 x) as,
${x}^{2}-8x+16-{y}^{2}$
$={x}^{2}-\left(2×4×x\right)+16-{y}^{2}$

Apply the formula $\left({a}^{2}-{b}^{2}\right)=\left(a-b\right)\left(a+b\right)$.
So,
${\left(x-4\right)}^{2}-{y}^{2}$
=(x-4+y)(x-4-y)
Step 4
Thus, the factor of the given polynomial is
(x-4+y)(x-4-y)

We have step-by-step solutions for your answer!