Question

Determine whether 81 − 49n^4 is a difference of two squares. If so, factor it. If not, explain why.

(9 + 7n^2 )(9 − 7n^2 )
(9 − 7n^2)(9 − 7n^2)
(9 − 7n^4)(9 + 7n^4)
Not a difference of squares because −49n^4 is not a perfect square.

Answer 1

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The given polynomial 81 − 49n⁴ is not a difference of two squares because −49n⁴ is not a perfect square.

We can see that 81 is a perfect square because it is equal to 9². However, 49n⁴ is not a perfect square because it can't be written as the square of a single term.

Therefore, we cannot factor 81 − 49n⁴ into the difference of two squares.