Factoring Formulas


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

$$a^{3}+3a^{2}b+3ab^{2}+b^{3} =(a+b)^{3}$$

$$a^{3}-3a^{2}b+3ab^{2}-b^{3} =(a-b)^{3}$$

$$a^{2n} -b^{2n} =(a^{n}-b^{n})(a^{n}+b^{n})$$


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