This is Algebra Formula Bank. So this Algebra Formula Bank provides all kinds of formula related to Algebra. Hope students find it useful.

#### Algebra Formula Bank

Here we give algebra formulas in different categories. Let’s see them one by one.

#### Square formula in Algebra

- 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
^{2}+ b^{2}= (a + b)^{2}– 2ab

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These are very basic and important formula in Algebra. Though these formulas are basic but they are very important while solving the problems in Algebra.

#### Square of Three Terms

- (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

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The next important category of formula in Algebra is cubic formula. So in this Algebra Formula Bank now we present the formula for cube.

- (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}

#### Some additional formula in the Algebra

These formulas have no frequent use in school level. However we use them in university level very much.

- (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})

#### Algebra Formula Collection for advance level

**If n is a natural number**, a^{n}– b^{n}= (a – b)(a^{n-1}+ a^{n-2}b+…+ 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 Indices

**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

In this expression the base a itself can never be zero.

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