How to Expand Double Brackets

Expanding Double Brackets

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.

Step-by-Step:

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.

We have written the double brackets as single brackets added together.

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 = x2

    x2

  • Multiply the second term inside the brackets (2) with the term outside the brackets (x), and add to the previous result

    x × 2 = 2x

    x2 + 2x

We have expanded the first single brackets

x(x + 2) = x2 + 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

We have expanded the second single brackets

1(x + 2) = x + 2

We have expanded all brackets.

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.

x2 + 2x + x + 2 = x2 + 3x + 2

Answer:

We have expanded the double brackets.

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See Also

What is algebra? What is a term? What is an expression? Multiplying letters Multiplying terms Expanding brackets Collecting like terms