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

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.