FREE WORKSHEET

Download Worksheet

The seven questions
shown on this page
can be downloaded
as a free worksheet

You can attempt
the questions yourself
and then
check your answers
against the results
shown on this page

Expand And Simplify
Two Sets Of Single Brackets

Expansion And Simplification Of Two Sets Of Single Parentheses In Algebra


Example 1
3(x + 2) + 5(x + 4)
= 3(x) + 3(+2) + 5(x) + 5(+4)
= 3x + 6 + 5x + 20
= 3x + 5x + 6 + 20
= 8x + 26

One way in which students understand more clearly
is to write in more positive signs

So we could get

3(x + 2) + 5(x + 4)
= +3(+x + 2) + 5(+x + 4)
= +3(+x) + 3(+2) + 5(+x) + 5(+4)
= +3x + 6 + 5x + 20
= +3x + 5x + 6 + 20
= +8x + 26
= 8x + 26

Example 2
3(x + 2) - 5(x + 4)
= 3(x) + 3(+2) - 5(x) - 5(+4)
= 3x + 6 - 5x - 20
= 3x - 5x + 6 - 20
= - 2x - 14

Example 3
3(x - 2) - 5(x + 4)
= 3(x) + 3(-2) - 5(x) - 5(+4)
= 3x - 6 - 5x - 20
= 3x - 5x - 6 - 20
= - 2x - 26

Example 4
3(x - 2) - 5(x - 4)
= 3(x) + 3(-2) - 5(x) - 5(-4)
= 3x - 6 - 5x + 20
= 3x - 5x - 6 + 20
= - 2x + 14

Example 5
- 3(x - 2) - 5(x - 4)
= - 3(x) - 3(-2) - 5(x) - 5(-4)
= - 3x + 6 - 5x + 20
= - 3x - 5x + 6 + 20
= - 8x + 26

Example 6
- 3(x - 2) - 5(-x - 4)
= - 3(x) - 3(-2) - 5(-x) - 5(-4)
= - 3x + 6 + 5x + 20
= - 3x + 5x + 6 + 20
= 2x + 26

Example 7
- 3(-x - 2) - 5(-x - 4)
= - 3(-x) - 3(-2) - 5(-x) - 5(-4)
= 3x + 6 + 5x + 20
= 3x + 5x + 6 + 20
= 8x + 26

Notice that this result
for the example
where all of the initial signs are negative
IS EXACTLY THE SAME RESULT
as when all of the initial signs are positive

The video shows examples
similar to those shown on this page
and also gives you examples to do
before the answers are shown

 

 

This Box Provides Dedicated Search Of YouTube

 

FREE WORKSHEET

Download Worksheet

The seven questions
shown on this page
can be downloaded
as a free worksheet

You can attempt
the questions yourself
and then
check your answers
against the results
shown on this page


Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.