Algebra Formulas

Alex robert

October 23, 2019 06:10:13 PM
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Algebra is a branch of Mathematics that substitutes letters for numbers. An algebraic equation depicts a scale, what is done on one side of the scale with a number is also done to either side of the scale. The numbers are constants. Algebra also includes real numbers, complex numbers, matrices, vectors and much more. X, Y, A, B are the most commonly used letters that represent the algebraic problems and equation 1b.

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Important Formulas in Algebra

Here is a list of Algebraic formulas –

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)
- am = 1a−m a−m = 1am
- If n is a natural number 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)
- If n is 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 + ….)
- Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn
- Fractional Exponents a0 = 1 aman=am−n am = 1a−m a−m = 1am
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