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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.
{\frac{1}{b}}
Algebra Formulas from Class 8 to Class 12
Algebra Formulas For Class 12
Algebra Formulas For Class 11
Algebra Formulas For Class 10
Algebra Formulas For Class 9
Algebra Formulas For Class 8
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
More topics in Algebra Formulas
Factoring Formulas Percentage Formula
Ratio Formula Matrix Formula
Exponential Formula Polynomial Formula
Standard Form Formula Direction of a Vector Formula
Interpolation Formula Sequence Formula
Direct Variation Formula Inverse Variation Formula
Equation Formula Series Formula
Function Notation Formula Foil Formula
Factoring Trinomials Formula Associative Property
Distributive Property Commutative Property
Complex Number Formula Profit Margin Formula
Gross Profit Formula Sum of Cubes Formula
Magnitude of a Vector Formula
Related Formulas
Anova FormulaAngle Formula
Area FormulasAntiderivative Formula
Area of a Sector FormulaArea of a Circle Formula
Area of an Octagon FormulaArea of a Segment of a Circle Formula