Algebra Formula – बीजगणित सूत्र
बीजगणित सूत्र (Algebra Formula)
- a2 – b2 = (a – b)(a + b)
- (a+b)2 = a2 + 2ab + b2
- a2 + b2 = (a – b)2 + 2ab
- (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)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- (a + b)3 = a3 + 3a2b + 3ab2 + b3
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
- a4 – b4 = (a – b)(a + b)(a2 + b2)
- a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
- प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
- सम संख्या (Even) – (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
- विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
- (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
- घातांक के नियम (Low Of Formula Exponents)
1. (am)(an) = am+n
2. (ab)m = ambm
3. (am)n = amn - (आंशिक घातांक) Fractional Exponents
1. a0 = 1
2. aman=am−naman=am−n
3. amam = 1a−m1a−m
4. a−ma−m = 1am
Some Product Formulas (कुछ गुणनफल सूत्र)
a2−b2=(a−b)(a+b)a2−b2=(a−b)(a+b)
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)
a4−b4=(a−b)(a+b)(a2−ab+b2)a4−b4=(a−b)(a+b)(a2−ab+b2)
a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)
(a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2
(a−b)2=a2−2ab+b2(a−b)2=a2−2ab+b2
(a+b)3=a3+3a2b+3ab2+b3(a+b)3=a3+3a2b+3ab2+b3
(a−b)3=a3−3a2b+3ab2−b3(a−b)3=a3−3a2b+3ab2−b3
(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
(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+…+2(ab+ac+bc+…)