Expanding Brackets in Algebra - Made Simple!

July 24, 2020
SAC Tutoring


Expanding the brackets in an algebraic equation leads us to two goals.. Getting rid of those brackets and simplifying!


Unfortunately it’s not as easy as just erasing those brackets. We need to do a series of multiplications.


There are two main ways to expand the brackets; double rainbow and FOIL.


Double Rainbow


This method is exactly what it sounds like! We have to draw two rainbows to get the terms out of the brackets.


Here we have a 4 outside the brackets and a + 7 inside the brackets.


  1. Draw two rainbows. One from the 4 to the a and one from the 4 to the 7

  1. Multiply the numbers between each rainbow

  1. Solve what you have

Nice and easy!


Here we have a 3 on the outside and 7b - 2 on the inside.

The thing to look out for here is that negative term in the bracket - the negative 2

 

1. Draw two rainbows

2. Multiply the numbers between each rainbow

Note: make sure you put negative numbers in brackets

positive 3 multiplied by negative 2 = negative 6

3. Solve what you have

 

DONE!

Here we have a negative 2x outside the bracket and a 9x - 2 inside the bracket.

Remember, - x - = +

 

1. Draw two rainbows

2. Multiply the numbers between each rainbow

3. Solve what you have

EZPZ!


FOIL Method

This method is used when you have two sets of brackets. I know, as if one set wasn't bad enough :(

Don't worry we have got your back.

FOIL stands for First, Outer, Inner and Last.

 

These refer to the terms in the brackets

 

(a + b)(c + d)

First refers to the first two terms. In this case, a and c.

Outer refers to the outer two terms. In this case, a and d.

Inner refers to the inner two terms. In this case, b and c.

Last refers to the last two terms. In this case, b and d.

 

 FIRST

OUTER

INNER

LAST 

 

After we have gotten our FOIL portion completed, all we have to do is put it all together!

 

Underlined in red here, we have like terms. This is where the last letter is the same in two or more terms. We can collect the like terms to simplify our answer.

 

After collecting the like terms, we are left with

And you're done!

All throughout high school, you're going to be seeing this method a lot. Make sure you are confident and comfortable with these techniques to ensure you do the best that you can!

 

Here at SAC, we are driven to make sure you are able to confidently tackle any problem and give you little tips and tricks to make studying easier.

 

Study smarter, not harder, with SAC!