This is an important part of simplification. In which some difficult problem are solved by using the algebraic formula
IMPORTANT FORMULA
1. $(a+b{)}^2=a^2+2ab+b^2=(a-b{)}^2+4ab$
2. $(a-b{)}^2=a^2-2ab+b^2=(a+b{)}^2-4ab$
3. $a^2+b^2=\frac{(a+b{)}^2+(a-b{)}^2}{2}$
4. $a^2-b^2=(a+b)(a-b)$
5. $(a+b{)}^3=a^3+b^3+3ab(a+b)$
6. $(a-b{)}^3=a^3-b^3-3ab(a-b)$
7.  $a^3+b^3=(a+b)(a^2-ab+b^2)$
8. $a^3-b^3=(a-b)(a^2+ab+b^2)$
9. $ab=\frac{(a+b{)}^2-(a-b{)}^2}{4}$
10. $(a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$
11. $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
12. $if a+b+c=0, then a^3+b^3+c^3=3abc$

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