Hi, I was having trouble with my maths homework. Here is a different version of my question: Simplify: 6a x -7. How would you figure this out? Thanks!I'm thinking the answer would be -43a. Is this...

Hi, I was having trouble with my maths homework. Here is a different version of my question:

Simplify: 6a x -7.

How would you figure this out? Thanks!

I'm thinking the answer would be -43a. Is this correct?

2 Answers | Add Yours

durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

6a x -7

The rules for multiplication and division differ from adding and subtracting where you can only add or subtract like terms. In this case, you multiply everything, such as you did. Care as 6 x 7 = 42

You will notice that whenever you multiply either 2 even numbers or one even and one odd you will always get an even answer - which will help you identify potential mistakes (6 is even so 43 (or any odd number) could never be the correct answer when multiplying!)

6a x -7

= -42a

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to perform the multiplication of numbers and multiplication of variables, using the laws of multiplication of negative numbers and the law of exponents, such that:

`6a x (-7)`

You may notice that multiplying ` -7` by 1 yields` -7` , hence, you may write the multiplication above such that:

6a x (-7*1)

You may convert 1 into a power, using the same variable a, such that:

`1 = a^0`

`6a X (-7*a^0)`

You need to perform the multiplication of numbers such that:

`6a X (-7*a^0) = (6 X (-7)) X a X a^0`

You need to perform the multiplication of powers using the following exponential law, such that:

`a x a^0 = a^(1+0) = a`

`(6 x (-7)) X a X a^0 = -42a`

Hence, performing the given multiplication yields `6a X (-7) = -42a.`

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