# Algebra

Friday 1st of January 2016

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This is an important part of simplification. In which some difficult problem are solved by using the algebraic formula
IMPORTANT FORMULA
1. $\left(a+b{\right)}^{2}={a}^{2}+2ab+{b}^{2}=\left(a-b{\right)}^{2}+4ab$
2. $\left(a-b{\right)}^{2}={a}^{2}-2ab+{b}^{2}=\left(a+b{\right)}^{2}-4ab$
3. ${a}^{2}+{b}^{2}=\frac{\left(a+b{\right)}^{2}+\left(a-b{\right)}^{2}}{2}$
4. ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)$
5. $\left(a+b{\right)}^{3}={a}^{3}+{b}^{3}+3ab\left(a+b\right)$
6. $\left(a-b{\right)}^{3}={a}^{3}-{b}^{3}-3ab\left(a-b\right)$
7.  ${a}^{3}+{b}^{3}=\left(a+b\right)\left({a}^{2}-ab+{b}^{2}\right)$
8. ${a}^{3}-{b}^{3}=\left(a-b\right)\left({a}^{2}+ab+{b}^{2}\right)$
9. $ab=\frac{\left(a+b{\right)}^{2}-\left(a-b{\right)}^{2}}{4}$
10. $\left(a+b+c{\right)}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2\left(ab+bc+ca\right)$
11. ${a}^{3}+{b}^{3}+{c}^{3}-3abc=\left(a+b+c\right)\left({a}^{2}+{b}^{2}+{c}^{2}-ab-bc-ca\right)$
12.