Draft:Remarkable identity

Squares of expression

• $(a\pm b{)}^2=a^2\pm 2ab+b^2$

1. $(a+b{)}^2=a^2+2ab+b^2$
2. $(a-b{)}^2=a^2-2ab+b^2$

• $a^2-b^2=(a-b)(a+b)$
• $a^2+b^2=(a\pm b{)}^2\pm 2ab$

1. $a^2+b^2=(a+b{)}^2-2ab$
2. $a^2+b^2=(a-b{)}^2+2ab$

Calculating Cube expressions

• $a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)$

1. $a^3+b^3=(a+b)(a^2-ab+b^2)$
2. $a^3-b^3=(a-b)(a^2+ab+b^2)$

• $(a\pm b{)}^3=a^3\pm 3a^{2}b+3a{b}^2\pm b^3$

1. $(a+b{)}^3=a^3+3a^{2}b+3a{b}^2+b^3$
2. $(a-b{)}^3=a^3-3a^{2}b+3a{b}^2-b^3$

Four-degree expression

• $(a\pm b{)}^4=a^4\pm 4a^{3}b+6a^2{b}^2\pm 4a{b}^3+b^4$

1. $(a+b{)}^4=a^4+4a^{3}b+6a^2{b}^2+4a{b}^3+b^4$
2. $(a-b{)}^4=a^4-4a^{3}b+6a^2{b}^2-4a{b}^3+b^4$

• $a^4-b^4=(a^2-b^2)(a^2+b^2)$

N degree expression

1. $a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}{b}^2+...+a^2{b}^{n-3}+a{b}^{n-2}+b[{\log }_{10}n-1-]$
2. $a^{2n}-b^{2n}=(a+b)(a^{2n-1}-a^{2n-2}b+a^{2n-3}{b}^2-...-a^2{b}^{2n-3}+a{b}^{2n-2}-b^{2n-1})$, burada $n\in N$
3. $a^{2n+1}+b^{2n+1}=(a+b)(a^{2n}+a^{2n-1}b+a^{2n-2}{b}^2-...-a^2{b}^{2n-2}+a{b}^{2n-1}-b^{2n})$, burada $n\in N$

with this type of attribute

• $(a-b{)}^{2n}=(b-a{)}^{2n}$, burada $n\in N$
• $(a-b{)}^{2n+1}=-(b-a{)}^{2n+1}$, burada $n\in N$

Also take a look

• Birhədli
• Çoxhədli