When multiplying a negative number an odd number of times, the answer is negative. When multiplying a negative number an even number of times, the answer is positive. Order of operations also applies: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. A mnemonic to remember the order of operations is “Please excuse my dear Aunt Sally.”

3(_–2)3 + (–_2)2

= 3(_–_8) + (4)

= _–_24 + 4

= _–_20

Two odd numbers multiplied always result in an even number. Simply multiple the two as though they were even. Thus

When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.

a3 + b2 becomes (–2)3 + (–3)2 which equals –8 + 9 = 1

Multiplying a negative number and another negative number makes the product positive.

First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.

Multiplying a negative and a positive number creates a negative product:

A negative number multiplied by a positive number will always be negative.