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 –
 a^{2} – b^{2} = (a – b)(a + b)
 (a + b)^{2} = a^{2} + 2ab + b^{2}
 a^{2} + b^{2} = (a + b)^{2}– 2ab
 (a – b)^{2} = a^{2} – 2ab + b^{2}
 (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca
 (a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab + 2bc – 2ca
 (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} ; (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
 (a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}= a^{3}– b^{3}– 3ab(a – b)
 a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})
 a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
 (a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4}
 (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4}
 a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})
 a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4})
 If n is a natural numbera^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+…+ b^{n2}a + b^{n1})
 If n is even (n = 2k), a^{n} + b^{n} = (a + b)(a^{n1}– a^{n2}b +…+ b^{n2}a – b^{n1})
 If n is odd (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +a^{n3}b^{2}… b^{n2}a + b^{n1})
 (a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + ….)
 Laws of Exponents (a^{m})(a^{n}) = a^{m+n} ; (ab)^{m} = a^{m}b^{m }; (a^{m})^{n} = a^{mn}
 Fractional Exponents a^{0} = 1 ;
\(\begin{array}{l}\frac{a^{m}}{a^{n}} = a^{mn}\end{array} \)
;\(\begin{array}{l}a^{m}\end{array} \)
=\(\begin{array}{l}\frac{1}{a^{m}}\end{array} \)
;\(\begin{array}{l}a^{m}\end{array} \)
=\(\begin{array}{l}\frac{1}{a^{m}}\end{array} \)
 Roots of Quadratic Equation
 For a quadratic equation ax^{2} + 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 = b^{2} − 4ac is called the discriminant
 For real and distinct roots, Δ > 0
 For real and coincident roots, Δ = 0
 For nonreal roots, Δ < 0
 If α and β are the two roots of the equation ax^{2} + 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
 For a quadratic equation ax^{2} + bx + c = 0 where a ≠ 0, the roots will be given by the equation as
 Factorials
 n! = (1).(2).(3)…..(n − 1).n
 n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
 0! = 1
\(\begin{array}{l}(a + b)^{n} = a^{n}+na^{n1}b+\frac{n(n1)}{2!}a^{n2}b^{2}+\frac{n(n1)(n2)}{3!}a^{n3}b^{3}+….+b^{n}, where\;,n>1\end{array} \)
Read more:
 Algebra
 Factorial
 Maths models
 Maths worksheets
Solved Examples
Example 1: Find out the value of 5^{2} – 3^{2}Solution:
Using the formulaa^{2} – b^{2} = (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: 4^{3}
\(\begin{array}{l}\times\end{array} \)
4^{2} = ?
Solution:
Using the exponential formula (a^{m})(a^{n}) = a^{m+n}where a = 4
4^{3}
\(\begin{array}{l}\times\end{array} \)
4^{2}= 4^{3+2}= 4^{5}= 1024More topics inAlgebra 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 ProfitFormula  Sum of Cubes Formula 
Magnitude of a Vector Formula 
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