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Expanding double brackets. Step by step guide on how to multiply out double brackets.

Updated on March 27, 2013

Expanding A Double Bracket Video

In the examples shown below we shall be expanding (multiplying out) double brackets. Be careful with the signs before the terms in the brackets.

Example 1

Expand and simplify (x+2)(x-5)

Multiply the first term in the first bracket by the first term in the second bracket.

x × x = x²

Multiply the first term in the first bracket by the second term in the second bracket.

x × -5 = -5x

Multiply the second term in the first bracket by the first term in the second bracket.

2 × x = 2x

Multiply the second term in the first bracket by the second term in the second bracket.

2 × -5 = -10

So you get:

x² -5x + 2x -10

Now all you need to do is simplify the middle two terms.

x² -3x -10

Example 2

Expand and simplify (3x - 5)(2x - 4)

Multiply the first term in the first bracket by the first term in the second bracket.

3x × 1x = 6x²

Multiply the first term in the first bracket by the second term in the second bracket.

3x × -4 = -12x

Multiply the second term in the first bracket by the first term in the second bracket.

-5 × 2x = -10x

Multiply the second term in the first bracket by the second term in the second bracket.

-5 × -4 = +20

So you get:

6x² -12x - 10x + 20

Now all you need to do is simplify the middle two terms.

6x² -22x + 20

If you need some more help on double bracket expanding then click here.

For some harder example on expanding double brackets then click here.

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