Multiply Out Two Brackets and Simplify

In this activity, we will be multiplying out two algebraic brackets.

 

Method

When we multiply out brackets, we need to multiply each term in the first bracket by each term in the second bracket.

 

To make sure that we don't forget any of the terms, we can use the word FOIL as a guide.

 

F = multiply the first term in each bracket.

O = multiply the outside term in each bracket.

I = multiply the inside term in each bracket.

L = multiply the last term in each bracket.

 

See how it works here:

 

 (a + b) (c + d) 

 

Apply FOIL:

F = first term which is a x c which we write as ac

O = outside which is a x d which we write as ad

I = inside which is b x c which we write as bc

L = last which is b x d which we write as bd

 

 

=  ac + ad + bc + bd

 

 

Examples

(x + 3) (x - 6) apply FOIL

 

F = x  times x = x²

O = x times -6 = -6x

I = 3 times x = 3x

L = 3 times -6 = -18

 

Collect like terms together:

x² - 6x  + 3x - 18

= x² - 3x - 18

(2x - 1)² 

This simply means the bracket squared:

(2x - 1) (2x - 1)

 

Apply FOIL

F = 2x times 2x = 4x²

O = 2x times -1 = -2x

I = -1 times 2x = -2x

L = -1 times -1 = 1

 

Collect like terms:

4x² -2x -2x + 1

= 4x² - 4x + 1

 

Are you ready to have a go at some questions? The important thing is to remember FOIL and apply it one step at a time.