# Expanding Brackets

"Expanding" means removing the ( )

Whatever is inside the ( ) needs to be treated as a "package". So when you multiply, you have to multiply by everything inside the "package".

• Created by: beaucaspa
• Created on: 18-02-14 13:49

## Expanding a single pair of brackets

Example 1 - Expanding a single pair of brackets

a) Expand: 3(x+6)  .

a) Remember to multiply every term inside the brackets by the term outside:

3(x+6)=3×x+3×6=3x+18  .

b) Expand: 6(4a10).

b) Remember to multiply every term inside the brackets by the term outside:

6(4a10)=24a60.

c) Expand: 3xy(2x+y2).

c) When multiplying more complicated terms, multiply the numbers first followed by the letters:

3xy(2x+y2)=6x2y+3xy3.

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## Expanding and simplifying brackets

Example 2 - Expanding and simplifying brackets

a) Expand and simplify 2(3x+4)+4(x1).

Multiply each bracket out first, then collect the like terms:

2(3x+4)+4(x1)=6x+8+4x4=10x+4

b) Expand and simplify 7(3n9)4(64n).

Be very careful when multiplying out brackets with lots of negative signs:

7(3n9)4(64n)=21n6324+16n=37n87

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## Expanding double brackets

### Example 3 - Expanding double brackets

Expand and simplify (a+b)(c+d).

When multiplying out double brackets, each terms in the first bracket must be multiplied by each term in the second:

(a+b)(c+d)=ac+ad+bc+bd.

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## Expandin and simplifying quadratic expressions

Example 4 - Expanding and simplifying quadratic expressions

a) Expand and simplify (x+4)(x+3).

When multiplying x by another x you will end up with an x2 term:

(x+4)(x+)x2+3x+4x+12 x2+7x+12

b) Expand and simplify (3x10)(5x9).

Remember, when multiplying two negative terms you will get a positive:

(3x10)(5x915x227x50x+90 15x277x+90

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