Important Formulas in Algebra
- a2-b2=(a-b)(a+b)
- (a+b)2=a2+2ab+b2
- (a-b)2=a2-2ab+b2
- a2+b2=(a-b)2+2ab
- (a+b+c)2=a2+b2+c2+2ab+2bc+2ca
- (a-b-c)2=a2+b2+c2-2ab+2bc-2ca
- (a+b)3=a3+3a2b+3ab2+b3 ; (a+b)3=a3+b3+3ab(a+b)
- (a-b)3=a3-3a2b+3ab2-b3 ; (a-b)3=a3-b3-3ab(a-b)
- a3-b3=(a-b)(a2+ab+b2)
- a3+b3=(a+b)(a2-ab+b2)
- (a+b)4=a4+4a3b+6a2b2+4ab3+b4
- (a-b)4-b4=(a-b)(a+b)(a2-b2)
- a5-b5=(a-b)(a4a3b+a2b2+ab3+b4)
- If n is natrural numberan-bn=(a-b)(an-1+an-2b+...+bn-2a+bn-1)
- If n is even (n=2k), an+bn=(a-b)(an-1+an-2b+...+bn-2a+bn-1)
- If n is odd (n=2k+1), an+bn=(a+b)(an-1+an-2b+an-3b...-bn-2+bn-1)
- (a+b+c)2=+ab2+b2+c2+...+2(ab+ac+bc+...)
- Laws of Exponent, (am)(an)=aam+n; (ab)m=ambm; (am)n=amn