How do you factor the difference of two squares? How do you factor the perfect square trinomial?How do you factor the sum and difference of two cubes?

Expert Answers
mathsworkmusic eNotes educator| Certified Educator

Write the difference of two squares as `a^2 -b^2`

This factors as `(a-b)(a+b)` . The mixed terms in `ab` cancel.

 

The perfect square trinomial can be written as

`x^2 + 2ax + a^2` which factors as `(x+a)(x+a)` (a perfect square)

The mixed terms takes the form `2ax`.

 

The sum of two cubes can be written as

`a^3 + b^3`

This factors as `(a+b)(a^2-ab+b^2) = a^3 - a^2b + ab^2 + a^2b - ab^2 +b^3 `

The mixed terms cancel by symmetry.

 

The difference of two cubes can be written as

`a^3 -b^3`

This factors as `(a-b)(a^2+ab+b^2) = a^3 + a^2b + ab^2 - a^2b-ab^2 - b^3 `

The mixed terms cancel be symmetry.