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
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.