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Which two of the following expressions are factors of a4 - 32a2 + 256

Sagot :

We need to factor in the next given expression:

[tex]a^4-32a^2+256[/tex]

Now, set u=a²

Then, we can rewrite the expression as:

[tex]u^2-32u+265[/tex]

The expression can be factor using the difference of squares:

[tex]=(u-16)(u+16)[/tex]

Use a²=u

[tex]=(a^2-16)(a^2+16)[/tex]

It can be simplified as:

[tex](a-4)^2(a+4)^2[/tex]

Hence, the factors are a+4 and a-4.

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