Expansion

 

Expansion is the process of removing the brackets in an expression and multiplying them term by term.

 

Example 1:

Take 4 and multiply it into every term inside the bracket, which in this case is 2x and 3. The product of 4 and 2x is 8x, and the product of 4 and 3 is 12.

After that, place your answers together, and you will get 8x + 12

 

 

Example 2:

 

Take the numbers in the first bracket and multiply them with every term in the second bracket individually. So, take x times y and the product will be xy , and multiply x to (-2) , the product being -(2x)

Later, multiply 3 to y , and the product is 3y and multiply 3 to 2 , and the product is 6 .    
So the answer will be xy - 2x + 3y -6
 

 

 

 

 

Both examples make use of the distributive law, where “a times b and c” is the same as “a times b” and “a times c”

 

Special identities can also be used for expansion

1. (a+b)² = a² + 2ab +b²

2. (a-b)² = a² - 2ab +b²

3. (a+b)(a-b) = a² + b²

Example 3:

(2x + 3)² = a² +2ab + b²                                                 a= 2x                                                         

              = (2x)² + 2(2x)(3) + 3²                                     b= 3

              = 4x² +12x + 9

 

Example 4:

(a + 2b)(a-2b) = a² + b²                                                 a= a

                      = a² - (2b)²                                              b= 2b

                      = a²-4b²