Factoring identities

d

Difference of squares

The difference of squares of quantities is equal to the product of their sum and difference.

$(1).\,\,$ $a^2-b^2$ $\,=\,$ $(a+b)(a-b)$

$(2).\,\,$ $x^2-y^2$ $\,=\,$ $(x+y)(x-y)$

Sum of cubes

$(1).\,\,$ $a^3+b^3$ $\,=\,$ $(a+b)(a^2+b^2-ab)$

$(2).\,\,$ $x^3+y^3$ $\,=\,$ $(x+y)(x^2+y^2-xy)$

Difference of cubes

$(1).\,\,$ $a^3-b^3$ $\,=\,$ $(a-b)(a^2+b^2+ab)$

$(2).\,\,$ $x^3-y^3$ $\,=\,$ $(x-y)(x^2+y^2+xy)$