In mathematics, Algebra is of the main parts of it. Algebra working with variables and numbers. Algebra is working with lots of formulas that relate two or more variables and numbers with each other.

## What is Formula?

A relationship between several variables can be expressed as a formula. The value of any variable of a formula can be found by substituting values for the other variables. The units of the values on two sides of the formula are the same, it is not necessary to state the units.

Here is a basic algebra formulas list.

## Algebra Formulas List

*(a + b) ^{2} = a^{2} + b^{2} + 2ab*

*(a – b) ^{2} = a^{2} + b^{2} – 2ab*

*a ^{2} – b^{2} = (a + b) (a – b)*

*a ^{2} + b^{2} = (a + b)^{2} – 2ab *

*or**a*

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

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

*2(a ^{2} + b^{2}) = (a+ b)^{2} + (a – b)^{2}*

*(a + b) ^{2} – (a – b)^{2} = 4ab*

*a ^{4} + b^{4} = (a + b) (a – b) [(a + b)^{2} – 2ab)]*

*(a – b) ^{2} = (a + b)^{2} – 4ab*

*(a + b) ^{2} = (a – b)^{2} + 4ab*

*a ^{4} + b^{4} = [(a + b)^{2} – 2ab]^{2} – 2(ab)^{2}*

*(a + b + c) ^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca*

*(a + b – c) ^{2} = a^{2} + b^{2} + c^{2} + 2ab – 2bc – 2ca*

*(a – b – c) ^{2} = a^{2} + b^{2} + c^{2} – 2ab + 2bc – 2ca*

*a ^{3} + b^{3} + c^{3} – 3abc = (a + b + c) (a^{2} + b^{2} + c^{2} – ab – bc – ca)*

*a ^{4} + a^{2}b^{2} + b^{4} = (a^{2} + ab + b^{2}) (a^{2} – ab + b^{2})*

*a ^{4} + a^{2} + 1 = (a^{2} + a + 1) (a^{2} – a + 1)*

if a + b + c = 0 then a^{3} + b^{3} + c^{3} = 3abc

a^{8} – b^{8} = (a^{4} + b^{4}) (a^{2} + b^{2}) (a + b) (a – b)

## Algebra Formulas With Examples

Example 01:

Find the value, **(27) ^{2}**

Instead of multiplying **27 x 27**, we can use the knowledge about algebraic formulas to find the value.

At once it may seem difficult than ordinary multiplication, but when you practice this method, you can find the value quickly.

**(27) ^{2} = (20 + 7)^{2}**

For this one you can use any two addictive bonds, but remember to use easier value that you are familiar with their squares.

We know the formula,*(a + b) ^{2} = a^{2} + 2ab + b^{2}*

When we consider **a = 20** and **b = 7**

(27)^{2}

= (20 + 7)^{2}

= (20)^{2} + 2 x 20 x 7 + (7)^{2}

= 400 + 280 + 49

= 729

Example 02:

Find the value, **(99) ^{2}**

For this one, we can use the formula** (a – b) ^{2}**

Although there are many ways to express

**99**, we can write

**99 = 100 – 1**

You may imagine how to take the exact two numbers. It will come to you with the practice.

We know that,*(a – b) ^{2} = a^{2} – 2ab + b^{2}*

In here, **a = 100** and **b = 1**

(99)^{2}

= (100 – 1)^{2} – 2 x 100 x 1 + (1)^{2}

= 10000 – 200 +1

= 9801

Example 03:

Let’s see an example we can use the algebraic formula **a ^{2} – b^{2}**

Find the value of **25 ^{2} – 12^{2}**

We know that,*a2 – b2 = (a + b) (a – b)*

In here **a=25** and **b = 12**

25^{2} – 12^{2}

= (25 + 12) (25 – 12)

= 37 x 13

= 481

## Download Algebra Formulas list PDF

Related Articles

Algebra Basics

The Pythagorean Theorem

## FAQ

### What is Formula?

A relationship between several variables can be expressed as a formula. The value of any variable of a formula can be found by substituting values for the other variables. The units of the values on two sides of the formula are the same, it is not necessary to state the units.

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