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 |
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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 – b3= 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 numberan – 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
- For a quadratic equation ax2 + 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
\(\begin{array}{l}(a + b)^{n} = a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+\frac{n(n-1)(n-2)}{3!}a^{n-3}b^{3}+….+b^{n}, where\;,n>1\end{array} \)
Read more:
- Algebra
- Factorial
- Maths models
- Maths worksheets
Solved Examples
Example 1: Find out the value of 52 – 32 \(\begin{array}{l}\times\end{array} \)
Solution:
Using the formulaa2 – b2 = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2
= 16
Example 2: 43
\(\begin{array}{l}\times\end{array} \)
42 = ? \(\begin{array}{l}\times\end{array} \)
Solution:
Using the exponential formula (am)(an) = am+n
where a = 4
43
= 43+2
= 45
= 1024
More 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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