Mathematics
- $a^2 – b^2 = (a – b)(a + b)$
-
$(a+b)^2 = a^2 + 2ab + b^2$
-
$a^2 + b^2 =(a+b)^2 - 2ab$
-
$(a-b)^2 = a^2 - 2ab + b^2$
-
$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$
-
$(a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca$
-
$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$
-
$(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
-
$(a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3$
-
$(a – b)^3 = a^3 – b^3 – 3ab(a – b)$
-
$a^3 – b^3 = (a – b)(a^2 + ab + b^2)$
-
$a^3 + b^3 = (a + b)(a^2 – ab + b^2)$
-
$(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$
-
$(a – b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4$
-
$a^4 – b^4 = (a – b)(a + b)(a^2 + b^2)$
-
$(a^m)(a^n) = a^{m+n}$
-
$(ab)^m = a^mb^m$
-
$(a^m)^n = a^{mn}$
-
$a^0 = 1 $
-
$a^m/a^n=a^{m-n}$
-
$a^m=1/a^{-m}$
-
$a^{-m}=1/a^m$