Question

How do you simplify `x^ 2 + x − 42 x^ 2 − x − 56`?

Answer 1

Shuffle the order of the terms around so the powers of `x` are in decreasing sequence and combine the coefficients to get:

`-41x^2 - 56`

Explanation:

`x^2+x-42x^2-x-56`

`=x^2-42x^2+color(red)(cancel(color(black)(x)))-color(red)(cancel(color(black)(x)))-56`

`=(1-42)x^2-56`

`=-41x^2-56`

This derivation uses some fundamental properties of addition and multiplication including:

Commutativity of addition and multiplication:

`color(white)(XX)a+b = b+a`

`color(white)(XX)ab = ba`

Distributivity:

`color(white)(XX)a(b+c) = ab+ac`