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

Sapewa 2021-12-15 Answered
Factor each polynomial.
x28x+16y2
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Expert Answer

Annie Gonzalez
Answered 2021-12-16 Author has 41 answers
Step 1
We need to factor the following polynomial
x28x+16y2
Step 2
The polynomial can be factored as following
x28x+16y2=(x28x+16)y2
=(x4)2y2
=[(x-4)-y][(x-4)+y] Using formula a2b2=(ab)(a+b)
=(x-4-y)(x-4+y)
Hence,
x28x+16y2=(x4y)(x4+y)

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Dabanka4v
Answered 2021-12-17 Author has 36 answers
Step 1
To find the factor of the given polynomial.
Step 2
Given information:
x28x+16y2
Step 3
Calculation:
Rewrite (8 x) as,
x28x+16y2
=x2(2×4×x)+16y2
=x2(2×4×x)+42Apply (ab)2 forμlay2
=(x4)2y2   [(ab)2=a22ab+b2]
Apply the formula (a2b2)=(ab)(a+b).
So,
(x4)2y2
=(x-4+y)(x-4-y)
Step 4
Thus, the factor of the given polynomial is
(x-4+y)(x-4-y)

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