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Expanding parentheses. How to multiply out a simple bracket.

Updated on June 19, 2013

How To Expand A Single Bracket Video


In math you will often have to multiply out parentheses (brackets). The correct name given to multiplying out a parenthesis is call expanding. The term at the start of the bracket must multiply the values inside the bracket. Let’s take a look at a few examples of multiplying out parentheses.

Example 1

Expand 3(2x + 4y)

The 3 at the start of the parenthesis must multiply both terms inside the bracket:

3 × 2x = 6x

3 × 4y = 12y

Putting these terms together gives a final expression of 6x + 12y.

Example 2

Expand 7(3x - 2y)

The 3 at the start of the parenthesis must multiply both terms inside the bracket:

7 × 3x = 21x

7 × -2y = -14y

Putting these terms together gives a final expression of 21x – 14y

Example 3

Expand -5(4k – 2z)

The -5 at the start of the parenthesis must multiply both terms inside the bracket:

-5 × 4k = -20k

-5 × -2z = 10z

Putting these terms together gives a final expression of -20k + 10z

Example 4

Expand x(x+4)

The x at the start of the parenthesis must multiply both terms inside the bracket:

x × x = x²

Make sure you remember that x times x is x squared

x × 4 = 4x

Putting these terms together gives a final expression of x² + 4x

Example 5

Expand 7x(9x + 4a)

The 7x at the start of the parenthesis must multiply both terms inside the bracket:

7x × 9x = 63x²

7x × 4a = 28ax

Make sure you put the letters in each term in alphabetical order.

Putting these terms together gives a final expression of 63x² + 28ax

Example 6

Expand 6(2x + 3y – 2x)

The 6 at the start of the parenthesis must multiply the three terms inside the bracket:

6 × 2x = 12x

6 × 3y = 18y

6 × -2x = -12x

Putting these terms together gives a final expression of 12x + 18y – 12x.

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