How do you factor 64z − z^3 64z−z3?

1 Answer
KillerBunny
Jun 15, 2016

z(8+z)(8-z)z(8+z)(8−z)

Explanation:

First of all, you can factor a zz, to obtain

z(64-z^2)z(64−z2)

Inside the parenthesis now we have the difference of two squares: we know that a^2-b^2=(a+b)(a-b)a2−b2=(a+b)(a−b), and thus

(64-z^2) = (8^2-z^2)=(8+z)(8-z)(64−z2)=(82−z2)=(8+z)(8−z)

Since now all three factors zz, 8+z8+z and 8-z8−z are linear (i.e. polynomials of first degree), we can no longer simplify the answer.

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