Factorization Formula

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 = a² + 2ab + b²

• (a − b)² = a²− 2ab + b²

• (a + b)³=a³ + b³ + 3ab (a + b)

• (a – b)³ = a³ – b³ – 3ab (a – b)

• (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

• (a − b)⁴ = a⁴ − 4a³b + 6a²b² − 4ab³ + b⁴

• (a + b + c)² = a² + b² +c² + 2ab + 2ac + 2bc

• a² – b²= (a + b) (a – b)

• a² + b² = (a + b)² – 2ab

• a³ – b³ = (a – b) (a² + ab + b²)

• a³ + b³ = (a + b) (a² – ab + b²)

Examples

Example 1

Factorize a²-625

a²-625 can be written as

a²-25² which is identical to a²-b²

a²-b²=(a+b)(a-b)

Hence, (a+25)(a-25) is the factored form of a²-625

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 = 2³*5 (Answer)