# Algebra - Product formulas

Real number : a,b,c
Whole numbers : n,k

1. $(a-b)^2=a^2+2ab+b^2$
2. $(a+b)^2=a^2+2ab+b^2$
3. $(a-b)^3=a^3-3a^2b+3ab^2-b^3$
4. $(a+b)^3=a^3+3a^2b+3ab^2+b^3$
5. $(a-b)^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4$
6. $(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4$
7. Binomial Formula
$(a+b)^2={^nC_0a^n}+{^nC_1a^{n-1}b}+{^nC_2a^{n-2}b^2}+...+{^nC_{n-1}ab^{n-1}}+{^nC_nb^n},$
Where $^nc_k={n! \over k!(n-k)!}$ are the binomial coefficients.
8. $(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc$
9. $(a+b+c+...+u+v)^2=a^2+b^2+c^3+...+u^2+v^2+2(ab+ac+...+au+av+ab+...+bu+bv+...+uv)$