Question

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

Answer 1

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

Explanation:

In order to factor `a^3 + b^3`
we must recognize that `a^3` is a perfect cube with a factor of `a`
and `b^3` is a perfect cube with a factor of `b`

The factor pattern for a binomial of perfect cubes is
`(a+b)(a^2 -ab +b^2)`
The factor of `a^3` and the factor of `b^3` go in the first parenthesis.
The second parenthesis has
the factor of `a^3` squared `(a^2)`
the factor of `a^3` times the factor of `b^3` `(ab)`
and the factor of `b^3` squared. `(b^2)`

For the signs we use the SOAP rule.

The First sign is the SAME as the sign in the binomial.
The Second sign is OPPOSITE of the sign in the binomial.
The Third sign is ALWAYS POSITIVE.

S- SAME
O- OPPOSITE
A- ALWAYS
P- POSITIVE