Distributive Property With Negative Numbers

When performing distribution, be enlightened of the sign beingness distributed and how that sign affects each term. Distributing a positive sign makes no difference in the signs of the terms — the signs stay the same. When distributing a negative sign, each term has a change of sign from negative to positive or from positive to negative.

Check out these examples to meet the distribution of positive and negative numbers in action, and notice how the terms do — or don't — change.

Distribute a positive number.

Example 1: +(fourx + twoy – 3z + 7) is the aforementioned as multiplying through by +one, and so

+1(iv10 + twoy – 3z + 7)

+ ane(fourx) + one(2y) + ane(–3z) + 1(7)

iv10 + 2y – 3z + 7

The signs don't modify.

Example 2 : +three(4x + 2y – 3z + 7)

+3(fourx) + 3(2y) + 3(–3z) + 3(vii)

12x + half-dozeny – ixz + 21

The signs don't alter.
Distribute a negative number.

Case ane : –(fourx + 2y – iiiz + vii) is the same as multiplying through by −one, and so

−1(4x + 2y – 3z + 7)

–one(410) –one(2y) –1(–3z) –ane(7)

–4ten – 2y + iiiz – 7

Each term changes to the opposite sign.

Example 2 : ivx(x – two) – (5x + 3)

fourten(x – 2) = 410(ten) – 4x(2)

–(5x + 3) = –(+vx) – (+3)

ivx(x) – 4x(2) – (+5ten) – (+3)

The catchy part is to make sure that you distribute the negative sign over the 510 and the 3.

1 mistake to avoid when you're distributing a negative sign is not distributing over all the terms. This is especially the instance when the process is hidden. Hidden ways that a negative sign may non be in front of the whole expression, where it stands out. It tin can be between terms, showing a subtraction and not being recognized for what information technology is. Don't let the negative signs ambush you.