How do you simplify $x^{2} + x - 42 x^{2} - x - 56$ $x^ 2 + x − 42 x^ 2 − x − 56$ ?

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Answer 1 · 2015-09-10T21:50:51

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

$- 41 x^{2} - 56$ $-41x^2 - 56$

$x^{2} + x - 42 x^{2} - x - 56$ $x^2+x-42x^2-x-56$

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

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

$=-41x^2-56$

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:

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

How do you simplify x^ 2 + x − 42 x^ 2 − x − 56x2+x−42x2−x−56x^ 2 + x − 42 x^ 2 − x − 56?