Factoring and Product Formulas
Factoring Formulas
a^2 – b^2 = (a-b)(a+b) |
a^3 – b^3 = (a-b)\left(a^2 + ab + b^2\right) |
a^3 + b^3 = (a+b)\left(a^2 – ab + b^2\right) |
a^4 – b^4 = (a-b)(a+b)\left(a^2 + b^2\right) |
a^5 – b^5 = (a-b)\left(a^4 + a^3b + a^2b^2 + ab^3 + b^4\right) |
Product Formulas
(a + b)^2 = a^2 + 2ab + b^2 |
(a – b)^2 = a^2 – 2ab + b^2 |
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 |
(a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3 |
(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 |
(a – b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4 |
(a + b + c)^2 = a^2 + b^2 + c^2 +2ab + 2ac + 2bc |
(a + b + c + …)^2 = a^2 + b^2 + c^2 + … + 2(ab + ac + bc + … ) |