Question

How do you factor `b^3-64c^3`?

Answer 1

Apply the difference of cubes formula to see that
`b^3-64c^3= (b - 4c)(b^2 + 4bc + 16c^2)`

Explanation:

The difference of cubes formula states that

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

(Verify this by multiplying out the right hand side)

Then, for the given expression, we have

`b^3-64c^3 = b^3-(4c)^3 = (b - 4c)(b^2 + 4bc + 16c^2)`

Answer 2

`b^3-64c^3=(b-4c)(b^2+4bc+16c^2)`

Explanation:

`b^3-64c^3` is a difference of cubes . The formula for factoring a difference of cubes is `(a-b)(a^2+ab+b^2)`, where `a=b` and `b=4c` in this case.

Substitute the values for `a and b` into the equation.

`(b-4c)(b^2+bxx4c+(4c)^2)`

Simplify.

`(b-4c)(b^2+4bc+16c^2)`