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 number a^{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 ; $\frac{a^{m}}{a^{n}} = a^{mn}$ ; $a^{m}$ = $\frac{1}{a^{m}}$ ; $a^{m}$ = $\frac{1}{a^{m}}$
 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 \(x=\frac{b\pm \sqrt{b^{2}4ac}}{2a}\)
 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
 Factorials

 n! = (1).(2).(3)…..(n − 1).n
 n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
 0! = 1
 \((a + b)^{n} = a^{n}+na^{n1}b+\frac{n(n1)}{2!}a^{n2}b^{2}+\frac{n(n1)(n2)}{3!}a^{n3}b^{3}+….+b^{n}, where\;,n>1\)
Solved Examples
Example 1: Find out the value of 5^{2} – 3^{2
}Solution:
Using the formula a^{2} – b^{2} = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 $\times$ 8
= 16
Example 2: 4^{3} $\times$ 4^{2} = ?
Solution:
Using the exponential formula (a^{m})(a^{n}) = a^{m+n }where a = 4
4^{3} $\times$ 4^{2 }= 4^{3+2 }= 4^{5 }= 1024
Using the formula a^{2} – b^{2} = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 $\times$ 8
= 16
Example 2: 4^{3} $\times$ 4^{2} = ?
Solution:
Using the exponential formula (a^{m})(a^{n}) = a^{m+n }where a = 4
4^{3} $\times$ 4^{2 }= 4^{3+2 }= 4^{5 }= 1024
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