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

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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.

 

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