Question

How do you factor `b^3 + 27`?

Answer 1

`b^3+27=(b+3)(b^2-3b+9)`

Explanation:

`b^3+27` is an example of a sum of cubes, where `a=b` and `b=3.`. Rewrite the expression as `(b)^3+(3)^3`.

To solve the sum of cubes, use the equation `a^3+b^3=(a+b)(a^2-ab+b^2)`.

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

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

Simplify.

`(b)^3+(3)^3=(b+3)(b^2-3b+9)`