To factorise a number, use the factorization formula. Factorization is the process of converting one thing into the product of another thing, or factors, that when multiplied together yield the original number.

## Definition

Factorization is a mathematical term that refers to a process of dividing down a large integer into smaller numbers that, when multiplied together, return the original number. These figures are divided into factors and divisors. Factorization Formula; N = X^{a}× Y^{b} × Z^{c}

Where,

N stands for a number,

X, Z, and Y are factors of number N

a, c, and b are exponents of factors.

## Factorization Formula List

There is a list of formulas which help to solve algebraic equations which are:

(a + b)

^{2}= a^{2}+ 2ab + b^{2}(a − b)

^{2}= a^{2}− 2ab + b^{2}(a + b)

^{3}=a^{3}+ b^{3}+ 3ab (a + b)(a – b)

^{3}= a^{3}– b^{3}– 3ab (a – b)(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 + b + c)

^{2}= a^{2}+ b^{2}+c^{2}+ 2ab + 2ac + 2bca

^{2}– b^{2}= (a + b) (a – b)a

^{2}+ b^{2}= (a + b)^{2}– 2aba

^{3}– b^{3}= (a – b) (a^{2}+ ab + b^{2})a

^{3}+ b^{3}= (a + b) (a^{2}– ab + b^{2})

## Examples

**Example 1**

**Factorize a ^{2}-625**

a^{2}-625 can be written as

a^{2}-25^{2} which is identical to a^{2}-b^{2}

a^{2}-b^{2}=(a+b)(a-b)

Hence, (a+25)(a-25) is the factored form of a^{2}-625

**Example 2**

**What is the prime factorization of 40?**

To find the prime factorization of 40 let’s break 40 = 2*2*2*5

Therefore, 40 = 2^{3}*5 (Answer)