Algebra Formulas

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 algebraic problems and equations.
Algebra Formulas from Class 8 to Class 12 Algebra Formulas For Class 8 Algebra Formulas For Class 9 Algebra Formulas For Class 10 Algebra Formulas For Class 11 Algebra Formulas For Class 12

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 + 2bc + 2ca
  • (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  • (a – b)3 = a3 – 3a2b + 3ab2 – b= a3 – b3 – 3ab(a – b)
  • 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
  • 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 +an-3b2…- 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 ;
    \(\begin{array}{l}\frac{a^{m}}{a^{n}} = a^{m-n}\end{array} \)
    ;
    \(\begin{array}{l}a^{m}\end{array} \)
    =
    \(\begin{array}{l}\frac{1}{a^{-m}}\end{array} \)
    ;
    \(\begin{array}{l}a^{-m}\end{array} \)
    =
    \(\begin{array}{l}\frac{1}{a^{m}}\end{array} \)
  • Roots of Quadratic Equation
    • For a quadratic equation ax2 + bx + c = 0 where a ≠ 0, the roots will be given by the equation as
      \(\begin{array}{l}x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end{array} \)
    • Δ = b2 − 4ac is called the discriminant
    • For real and distinct roots, Δ > 0
    • For real and coincident roots, Δ = 0
    • For non-real roots, Δ < 0
    • If α and β are the two roots of the equation ax2 + bx + c = 0 then, α + β = (-b / a) and α × β = (c / a).
    • If the roots of a quadratic equation are α and β, the equation will be (x − α)(x − β) = 0
  • Factorials
    • n! = (1).(2).(3)…..(n − 1).n
    • n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
    • 0! = 1
    • \(\begin{array}{l}(a + b)^{n} = a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+\frac{n(n-1)(n-2)}{3!}a^{n-3}b^{3}+….+b^{n}, where\;,n>1\end{array} \)

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Solved Examples

Example 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 
\(\begin{array}{l}\times\end{array} \)
8
= 16

Example 2:
43
\(\begin{array}{l}\times\end{array} \)
42 = ?
Solution:
Using the exponential formula (am)(an) = am+n
where a = 4
43
\(\begin{array}{l}\times\end{array} \)
4
2
= 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

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