Multiplication of algebra expressions

When we multiply algebraic expressions, we need to remember the Index Laws from the Numbers chapter.

Let's see how algebra multiplication works with a series of examples.

Example 1

Multiply x³(x⁴ + 5a)

Answer

We expand this out using the distributive law:

x³(x⁴ + 5a)
= x⁷ + 5ax³

We cannot simplify this answer any further. We present our answer in alphabetical order since it makes it easier to read when the problems become more involved.

Example 2

Multiply (x + 5)(a − 6)

Answer

We multiply this out as follows. We take each term of the first bracket and multiply them by the second bracket. Then we expand out the result.

(x + 5)(a − 6)
= x(a − 6) + 5(a − 6)
= ax − 6x + 5a − 30

We cannot do any more with this answer. There are no like terms, so we cannot simplify it in any way.

Example 3

Multiply (2x + 3)(x² − x − 5)

Show answer

We take the 2 terms of the first bracket and multiply both of them by the second bracket.
(2x + 3)(x²− x − 5)
= (2x)(x² − x − 5) + (3)(x² − x − 5)

= (2x³ − 2x² − 10x) + (3x² − 3x − 15)

= 2x³ + x² − 13x − 15
This time we could collect together some like terms. There was:

−2x² + 3x² = x²

and

−10x − 3x = −13x

Share on Google Plus

About Unknown

This is a short description in the author block about the author. You edit it by entering text in the "Biographical Info" field in the user admin panel.