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2 years ago

Determine whether 81 − 49n4 is a difference of two squares. If so, factor it. If not, explain why.

Mathematics

1 answer:

Mumz [18]2 years ago

7 0

We have

$81-49n^4=9^2-(7n^2)^2$

so this is indeed a difference of squares. Factorizing would give

$81-49n^4=(9-7n^2)(9+7n^2)$

making the answer D.

We can further factor the first term here and write

$9-7n^2=3^2-(\sqrt 7\,n)^2=(3-\sqrt7\,n)(3+\sqrt7\,n)$

but that's clearly out of the scope of this question.

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Step-by-step explanation:

Please see the picture below.

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