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:


c) Expand: 3xy(2x+y2).

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


1 of 4

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:


b) Expand and simplify 7(3n9)4(64n).

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


2 of 4

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:


3 of 4

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

4 of 4


No comments have yet been made

Similar Mathematics resources:

See all Mathematics resources »See all Algebra resources »