# 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.

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Algebra Formulas from Class 8 to Class 12 |
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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**–

- 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 + 2ac + 2bc - (a – b – c)
^{2}= a^{2}+ b^{2}+ c^{2}– 2ab – 2ac + 2bc - (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}= (a – b)(a^{2}+ ab + b^{2}) - a
^{3}+ b^{3}= (a + b)(a^{2}– ab + b^{2}) - (a + b)
^{3}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3} - (a – b)
^{3}= a^{3}– 3a^{2}b + 3ab^{2}– b^{3} - (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^{n-1}+ a^{n-2}+…+ b^{n-2}a + b^{n-1})**If n is even**(n = 2k), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +…+ b^{n-2}a – b^{n-1})**If n is odd**(n = 2k + 1), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +…- b^{n-2}a + b^{n-1})- (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

$\frac{a^{m}}{a^{n}} = a^{m-n}$

$a^{m}$ = $\frac{1}{a^{-m}}$^{ }$a^{-m}$ = $\frac{1}{a^{m}}$

### Solved Examples

**Question 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

**4**

Question 2:

Question 2:

^{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

Related Formulas | |

Anova Formula | Angle Formula |

Area Formulas | Antiderivative Formula |

Area of a Sector Formula | Area of a Circle Formula |

Area of an Octagon Formula | Area of a Segment of a Circle Formula |