Question

factor b^3-125

Answer 1

First thing you need to do is notice that \[125 = 5^{3}\], giving you a difference of cubes.
You then use the difference of cubes equation:
\[a ^{3} – b ^{3} = (a – b)(a ^{2} + ab + b ^{2})\]

Where a = b and b = 5 (kind of confusing with your initial value being b)

So you should end up with \[(b – 5)(b ^{2} + 5b + 25)\]
And when factoring difference of cubes, they factor in such a way that the second term cannot be factored any further.

Answer 2

A3 - B3 = (A - B)(A2 + AB + B2 )
b^3 - 5^3 = (b-5)(b^2 + 5b + 5^2)

Answer 3

\[A^3 - B^3 = (A - B)(A^2 + AB + B^2 )\]
\[b^3 - 5^3 = (b-5)(b^2 + 5b + 5^2) \]