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

1 Answer
Sep 10, 2015

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#