Quadratics

Factoring with difference of squares and Perfect squares

 

Perfect squares and diffence of squares a special type of way of factoring  

 

 

Lets start with difference of squares (a+b)(a-b) = a^2 -b^2

Both a^2 and b^2 need to be perfect squares and the equation must have negative integer 

 

For example : 9x^2- 16= (3x+4) (3x-4)

 

All you have to do is find the square root of 9 and put it in each bracket along with the variable and find the root of 16

make one positive and one negative and place one in each bracket

If you are givrn the factored form you can easily work backwards and find the equation in standard form

(4x+7)(4x-7) you can easily expand the bracket or even tell by looking at it that 4x4 and 7x-7= 16x^2 -49 

 

 

 

Perfect squares a^2 + 2ab + b^2 = (a+b)^2 and a^2-2ab+b^2 = (a-b)^2 

 

Perfect squares are alot like difference of squares 

They follow these rules: 

1: First and last terms are perfect squares

2: The middle term is twice the product of the square roots of the first and last term

 

4x^2 + 20x + 25 

2x5 = 10x2 = 20 Therefore it is a perfect square

 

When you know something is a perfect square you find the roots of the first and last term and place them in the bracket

4x^2 + 20x + 25 = (2x+5)^2 

 

 

 

 

 

For more help with factoring squares !