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Expanding Double Brackets
(KS3, Year 8)
The Lesson
Double brackets are two brackets written next to each other. The two brackets are multiplying each other.Expanding double brackets means multiplying terms in the pair of expressions to remove the brackets. Imagine we wanted to remove the brackets from the pair of expressions below. We have to expand the brackets.
How to Expand Double Brackets
Expanding double brackets is easy.Question
Expand the double brackets below.StepbyStep:
1
Write the first term in the first brackets (x) in front of the second brackets (x + 2).
x(x + 2)
2
Write the second term in the first brackets (1) in front of the second brackets (x + 2), and add to the previous result.
x(x + 2) + 1(x + 2)
Note: The term is added because there is a + before the second term in the first brackets.
3
Expand the first single brackets, x(x + 2).

Multiply the first term inside the brackets (x) with the term outside the brackets (x).
x × x = x^{2} x^{2}

Multiply the second term inside the brackets (2) with the term outside the brackets (x), and add to the previous result
x × 2 = 2x x^{2} + 2x
x(x + 2) = x^{2} + 2x
4
Expand the second single brackets, 1(x + 2).

Multiply the first term inside the brackets (x) with the term outside the brackets (1).
1 × x = x x

Multiply the second term inside the brackets (2) with the term outside the brackets (1), and add to the previous result.
1 × 2 = 2 x + 2
1(x + 2) = x + 2
5
Replace the single brackets with their expansions.
6
Simplify the expression if necessary by collecting like terms together. In our example, we can collect the x terms together.
x^{2} + 2x + x + 2 = x^{2} + 3x + 2
Answer:
We have expanded the double brackets.Multiplication Tips

Multiplying a number with a variable
2 × x = 2x 5 × x = 5x

Multiplying a number with a variable with a coefficient
2 × 2x = 4x 3 × 5x = 15x

Multiplying a variable with a variable
x × y = xy x × x = x^{2}
Beware
Be Careful with Signs
Each term in the brackets will have a sign. positive terms have a + sign in front of them, or no sign if it is the first term.
 negative terms have a − sign in front of them.
Remember the rules for multiplying different signs: Same signs give a plus:
Different signs give a minus:
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