Simplifying and index laws

The idea

Like terms have the same letters and powers, so they combine: $3x + 5x = 8x$, but $3x + 5x^2$ cannot. Index laws: $x^a \times x^b = x^{a+b}$, $x^a \div x^b = x^{a-b}$ and $(x^a)^b = x^{ab}$.

1. Group like terms, keeping the sign in front of each.
2. Multiply the numbers, then add the powers of each letter.
3. $(2x^3)^2 = 4x^6$: square the $2$ as well.

Watch out $x^3 \times x^4 = x^7$, not $x^{12}$.