Algebra Formulas

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 \(\large \frac{1}{b}\).
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)
            • 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
              $\frac{a^{m}}{a^{n}} = a^{m-n}$
              $a^{m}$ = $\frac{1}{a^{-m}}$
              $a^{-m}$ = $\frac{1}{a^{m}}$

Solved Examples

Question 1: Find out the value of 52 – 32
Solution:
Using the formula a2 – b2 = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 $\times$ 8
= 16

Question 2:
43 $\times$ 42 = ?
Solution:
Using the exponential formula (am)(an) = am+n
where a = 4
43 $\times$ 42
= 43+2
= 45
= 1024

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Practise This Question

Simplify (67)2×(76)2