Negative Signs and Parentheses

The distributive property is a source of many mistakes in algebra. When a negative sign, multiplication, or division is next to a set of parentheses, everything inside the parentheses will be affected.

Negative signs in particular bother many students. The most reliable approach is probably to rewrite subtraction as the addition of a negative, then distribute the negative sign to all terms inside the parentheses.

The answer shown below is wrong.  Try working your way through the problem backwards, from the answer up. As you find each mistake, try to identify the thinking behind it… what perspective led to the mistake? What should have been done instead?

(1-d+e)-(2d-3e+4)-(-4e+3d-2)

=(1-d+e)-(-2d+3e-4)+(4e-3d-2)$

=1-d+e+2d-3e+4+4e-3d-2

=-d+2d-3d+e-3e+4e+1+4-2

=-6d+2e+3

.

..

Hint 1: the correct answer to the original problem is: 8e-6d-1

Hint 2: a number of mistakes have been made in the work above – they are not all sign errors. Identify all of the errors made at each step and the likely reasons they were made before solving the problem correctly yourself.

Published by

Whit Ford

Math teacher, substitute teacher, and tutor (along with other avocations)

2 thoughts on “Negative Signs and Parentheses”

    1. Harold,

      Thank you for your question! I checked the answer, and it was indeed wrong. The correct answer should be
      8c-6d-1
      The constant term is the result of adding 1, -4, and 2 (after distributing the negative signs and dropping the parentheses in the original problem as stated on the first line).

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