Multiplying Expressions in Algebra
(KS3, Year 8)

The Lesson

Expressions can be multiplied. Imagine we wanted to multiply the expressions x + 1 and 3 − y.

How to Multiply Expressions in Algebra

Multiplying expressions in algebra is easy.

Question

Multiply the expressions below.

Step-by-Step:

1

Put brackets around each expression and write them next to each other.

2

Expand the double brackets. Use the FOIL method to expand the brackets.
x2 Firsts \(\:\:\:\:\:\:\:\:\:\:\:\:\) (x + 1)(x + 2) \(\:\:\:\:\:\:\:\:\:\:\:\:\) x × x
x2 + 2x Outsides \(\:\:\:\:\:\:\) (x + 1)(x + 2) \(\:\:\:\:\:\:\:\:\:\:\:\:\) x × 2
x2 + 2x + x Insides \(\:\:\:\:\:\:\:\:\:\) (x + 1)(x + 2) \(\:\:\:\:\:\:\:\:\:\:\:\:\) 1 × x
x2 + 2x + x + 2 Lasts \(\:\:\:\:\:\:\:\:\:\:\:\:\) (x + 1)(x + 2) \(\:\:\:\:\:\:\:\:\:\:\:\:\) 1 × 2

3

Simplify the expression if necessary by collecting like terms together. In our example, we can collect the x terms together.
x2 + 2x + x + 2 = x2 + 3x + 2

Answer:

We have multiplied the expressions.

Lesson Slides

The slider below shows another real example of how to multiply expressions in algebra. Open the slider in a new tab

To Expand or Not to Expand? That Is the Question

To multiply expressions, put each expression in a bracket and write them next to each other.
x + 1 × x + 3 = (x + 1)(x + 3)
This product of two brackets may be the simplest way to write the answer. The brackets can then be expanded. Whether to do this or not depends on context. Imagine having multiplied the expressions above, we then subtract another term...
(x + 1)(x + 3) − 8x
...then it is worth expanding the brackets...
x2 + 4x + 3 − 8x
Collecting like terms...
x2 − 4x + 3
...and factoring...
x2 − 4x + 3 = (x − 1)(x − 3
The moral is that multiplying expressions is yet another tool in the algebra toolbox. How you use it, and what other tools you use, depends on what job you are trying to do.
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See Also

What is algebra? What is an expression? What is a term? Expanding brackets Expanding double brackets What is the FOIL method? Collecting like terms