Factoring formulas
Difference of two squares
$$a^{2} -b^{2} =(a-b)(a+b)$$
Perfect square trinomials
$$a^{2}+2ab+b^{2} =(a+b)^{2}=(-a-b)^{2}$$
$$a^{2}-2ab+b^{2}=(a-b)^{2}=(b-a)^{2}$$
Sum of two cubes
$$a^{3} +b^{3} =(a+b)(a^{2}-ab+b^{2})$$
Difference of two cubes
$$a^{3} -b^{3} =(a-b)(a^{2}+ab+b^{2})$$
Other factoring formulas
$$a^{3}+3a^{2}b+3ab^{2}+b^{3} =(a+b)^{3}$$
$$a^{3}-3a^{2}b+3ab^{2}-b^{3} =(a-b)^{3}$$
$$a^{2n} -b^{2n} =(a^{n}-b^{n})(a^{n}+b^{n})$$
Factoring Formulas FAQ
What are factoring formulas?
Factoring formulas rewrite expressions as products of simpler factors.
Which factoring patterns are shown here?
The page covers difference of squares, perfect square trinomials, and sums and differences of cubes.
