Expand and Simplify

How to Expand

Question
Expand   3(x + 2)

"Expand" means you must multiply out the brackets. You need to times everything inside the brackets (i.e. x + 2) by what's outside the brackets (3).

3(x + 2) = 3x + 6

Try these:

Expand
a) 2(x - 1)
b) 5(2 - x)
c) x(x + 3)

Did you get...?

a) 2(x - 1) = 2x - 2
b) 5(2 - x) = 10 - 5x
c) x(x + 3) = x^2 + 3x


Expand and Simplify


"Simplify" means you must write your answer as simply as possible.

For example, if you have an expression such as

3x + 2 + x + 1

you can add together the like-terms (add together the "x terms" and the number terms)

3x + 2 + x + 1 = (3x + x) + (2 + 1) = 4x + 3


In your exam, you will probably get a question like this:

Question
Expand and Simplify   2(x + 1) + 3(x - 2)

You must first expand out the brackets, and then simplify (add the like-terms):

Solution

 2(x + 1) + 3(x - 2)
= 2x + 2 + 3x - 6
= 2x + 3x + 2 - 6
= 5x - 4


Try these:

Expand and simplify
a) 2(x - 1) + 5(2 - x)
b) 7(x + 3) + 2(x + 2)

Did you get...?

a) 2(x - 1) + 5(2 - x)
= 2x - 2 + 10 - 5x
= 2x - 5x - 2+ 10
= - 3x + 8


*Remember*  -2 + 10 = 10 - 2 = 8




b) 7(x + 3) + 2(x + 2) 
= 7x + 21 + 2x + 4
= 7x + 2x + 21 + 4
= 9x + 25


Remember:
Don't forget to multiply everything inside the brackets by the outside value. One of the most common mistakes is as follows:

3(x + 2) = 3x + 2
This is NOT CORRECT, as we have not multiplied the 2 by the 3.

3(x + 2) = 3x + 6 is correct.


Top Tip
Be careful with questions such as

Expand and Simplify   3(x + 1) - 2(x + 1)

where the two expressions in the brackets have a minus sign (-) between them. In this case, expand the brackets, but keep the second expression separate, like this:

3(x + 1) - 2(x + 1)
= 3x + 3 - [2x + 2]

Then you must take away the right-hand expression from the left:

= 3x + 3 - [2x + 2]
= 3x - 2x + 3 - 2
= x + 1