Question

Determine whether 81a^2 − 25z^6 is a difference of two squares. If so, factor it. If not, explain why.

(9a − 5z^3)(9a − 5z^3)
(9a + 5z^3)(9a − 5z^3)
(9a − 5z^6)(9a + 5z^6)
It is not a difference of squares because −25z^6 is not a perfect square.

Answer 1

The given polynomial 81a² − 25z⁶ is not a difference of two squares because −25z⁶ is not a perfect square.

We can see that 81a² is a perfect square because it is equal to (9a)². However, 25z⁶ is not a perfect square because it can't be written as the square of a single term.

Therefore, we cannot factor 81a² − 25z⁶ into the difference of two squares.

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