In algebra, a binomial is a polynomial with exactly two terms, such as (a + b). Expanding binomials—specifically squaring or cubing them—is a fundamental skill used to simplify complex equations.

Instead of multiplying the brackets manually every time, we use specific patterns known as Special Products to find the answer quickly.

Key Formulas:

Square of a Sum:

Square of a Difference:

Cube of a Sum:

Cube of a Difference:

The best Maths tutors available
Paolo
4.9
4.9 (78 reviews)
Paolo
£35
/h
Gift icon
1st lesson free!
Intasar
5
5 (69 reviews)
Intasar
£129
/h
Gift icon
1st lesson free!
Sehaj
4.9
4.9 (56 reviews)
Sehaj
£60
/h
Gift icon
1st lesson free!
Johann
5
5 (48 reviews)
Johann
£60
/h
Gift icon
1st lesson free!
Hiren
5
5 (32 reviews)
Hiren
£149
/h
Gift icon
1st lesson free!
Poonam
5
5 (62 reviews)
Poonam
£100
/h
Gift icon
1st lesson free!
Harjinder
4.9
4.9 (163 reviews)
Harjinder
£25
/h
Gift icon
1st lesson free!
Syed
5
5 (69 reviews)
Syed
£50
/h
Gift icon
1st lesson free!
Paolo
4.9
4.9 (78 reviews)
Paolo
£35
/h
Gift icon
1st lesson free!
Intasar
5
5 (69 reviews)
Intasar
£129
/h
Gift icon
1st lesson free!
Sehaj
4.9
4.9 (56 reviews)
Sehaj
£60
/h
Gift icon
1st lesson free!
Johann
5
5 (48 reviews)
Johann
£60
/h
Gift icon
1st lesson free!
Hiren
5
5 (32 reviews)
Hiren
£149
/h
Gift icon
1st lesson free!
Poonam
5
5 (62 reviews)
Poonam
£100
/h
Gift icon
1st lesson free!
Harjinder
4.9
4.9 (163 reviews)
Harjinder
£25
/h
Gift icon
1st lesson free!
Syed
5
5 (69 reviews)
Syed
£50
/h
Gift icon
1st lesson free!
Let's go

Worked Example

Expand the following expression:

Solution: Here, a = 2x and b = 3. We use the Square of a Sum formula.

Practice Questions & Solutions

1

Expand:

Solution

2

Expand:

Solution

3

Expand:

Solution

4

Expand:

Solution

5

Expand:

Solution

6

Expand:

Solution

7

Expand:

Solution

8

Expand:

Solution

9

Expand:

Solution

10

Expand:

Solution

Did you like this article? Rate it!

4.00 (8 rating(s))
Loading...

Gianpiero Placidi

UK-based Chemistry graduate with a passion for education, providing clear explanations and thoughtful guidance to inspire student success.