Question

hello this is math 80 intermediate algebra i cant figure out why we have to put 16 and not 64. the question is 64-r^3 the answer is 16+4r+r^2 but I put 64+4r+r^2...

Answer 1

Answer:

$\begin{equation*} (4-r)(16+4r+r^2) \end{equation*}$

Explanation:

Given:

$64-r^3$

To factor the above binomial completely, we'll first rewrite it as seen below;

$64-r^3=4^3-r^3$

Recall the difference cubes formula below;

$a^3-b^3=(a-b)(a^2+ab+b^2)$

If we compare both expressions, we can see that a = 4 and b = r, so we we'll have;

$4^3-r^3=(4-r)(4^2+4r+r^2)=(4-r)(16+4r+r^2)$