Algebra formulas

Algebra Formulas

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 = a2 + b2 + 2ab

(a – b)2 = a2 + b2 – 2ab

a2 – b2 = (a + b) (a – b)

a2 + b2 = (a + b)2 – 2ab or a2 + b2 = (a – b)2 + 2ab

a3 + b3 = (a + b) (a2 – ab + b2) = (a + b)3 – 3ab(a + b)

a3 – b3 = (a – b) (a2 + ab + b2) = (a – b)3 + 3ab(a – b)

2(a2 + b2) = (a+ b)2 + (a – b)2

(a + b)2 – (a – b)2 = 4ab

a4 + b4 = (a + b) (a – b) [(a + b)2 – 2ab)]

(a – b)2 = (a + b)2 – 4ab

(a + b)2 = (a – b)2 + 4ab

a4 + b4 = [(a + b)2 – 2ab]2 – 2(ab)2

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

(a + b – c)2 = a2 + b2 + c2 + 2ab – 2bc – 2ca

(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca

a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)

a4 + a2b2 + b4 = (a2 + ab + b2) (a2 – ab + b2)

a4 + a2 + 1 = (a2 + a + 1) (a2 – a + 1)
if a + b + c = 0 then a3 + b3 + c3 = 3abc
a8 – b8 = (a4 + b4) (a2 + b2) (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 = a2 + 2ab + b2

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 = a2 – 2ab + b2

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 a2 – b2

Find the value of 252 – 122

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

In here a=25 and b = 12
252 – 122
= (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.

Algebra Formulas List

algebraic formulas list

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