farmula of algebra
math
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Answer:
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Step-by-step explanation:
Algebraic Formulas & Expression
a2−b2=(a+b)(a−b)a2−b2=(a+b)(a−b)
(a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2
a2+b2=(a−b)2+2aba2+b2=(a−b)2+2ab
(a−b)2=a2−2ab+b2(a−b)2=a2−2ab+b2
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc(a+b+c)2=a2+b2+c2+2ab+2ac+2bc
(a−b−c)2=a2+b2+c2−2ab−2ac+2bc(a−b−c)2=a2+b2+c2−2ab−2ac+2bc
(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)
(a−b)3=a3−3a2b+3ab2−b3(a−b)3=a3−3a2b+3ab2−b3
a3−b3=(a−b)(a2+ab+b2)a3−b3=(a−b)(a2+ab+b2)
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=a4+4a3b+6a2b2+4ab3+b4
(a−b)4=a4−4a3b+6a2b2−4ab3+b4(a−b)4=a4−4a3b+6a2b2−4ab3+b4
a4−b4=(a−b)(a+b)(a2+b2)a4−b4=(a−b)(a+b)(a2+b2)
a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)
(x+y+z)2=x2+y2+z2+2xy+2yz+2xz(x+y+z)2=x2+y2+z2+2xy+2yz+2xz
(x+y−z)2=x2+y2+z2+2xy−2yz−2xz(x+y−z)2=x2+y2+z2+2xy−2yz−2xz
(x−y+z)2=x2+y2+z2−2xy−2yz+2xz(x−y+z)2=x2+y2+z2−2xy−2yz+2xz
(x−y−z)2=x2+y2+z2−2xy+2yz−2xz(x−y−z)2=x2+y2+z2−2xy+2yz−2xz
x3+y3+z3−3xyz=(x+y+z)(x2+y2+z2−xy−yz−xz)x3+y3+z3−3xyz=(x+y+z)(x2+y2+z2−xy−yz−xz)
x2+y2=12[(x+y)2+(x−y)2]x2+y2=12[(x+y)2+(x−y)2]
(x+a)(x+b)(x+c)=x3+(a+b+c)x2+(ab+bc+ca)x+abc(x+a)(x+b)(x+c)=x3+(a+b+c)x2+(ab+bc+ca)x+abc
x3+y3=(x+y)(x2−xy+y2)x3+y3=(x+y)(x2−xy+y2)
x3−y3=(x−y)(x2+xy+y2)x3−y3=(x−y)(x2+xy+y2)
x2+y2+z2−xy−yz−zx=12[(x−y)2+(y−z)2+(z−x)2]x2+y2+z2−xy−yz−zx=12[(x−y)2+(y−z)2+(z−x)2]
If n is a natural number, an−bn=(a−b)(an−1+an−2b+...+bn−2a+bn−1)an−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)(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+...−bn−2a+bn−1)(n=2k+1),an+bn=(a+b)(an−1−an−2b+...−bn−2a+bn−1)
(a+b+c+...)2=a2+b2+c2+...+2(ab+bc+....)