# a2 – b2 Formula

Last Updated : 24 Jan, 2024

a2 – b2 formula in Algebra is the basic formula in mathematics used to solve various algebraic problems. a2 – b2 formula is also called the difference of square formula, as this formula helps us to find the difference between two squares without actually calculating the squares. The image added below shows the formula of a2 – b2

In this article, we will learn the a2 – b2 formula, a2 – b2 identity, examples, and others in detail.

## What is a2 – b2 Formula?

a2 – b2 formula in algebra is the basic formula to solve algebraic problems. It is also used to solve trigonometric, differential, and other problems. This formula tells us that the difference between square two numbers is equal to the product of the sum and difference of two numbers, i.e.

a2 – b2 = (a + b).(a – b)

### a2 – b2 Formula Definition

The formula a2 – b2 allows us to determine the variance between the squares of two numbers without the need to compute the actual square values. The expression for the a2 – b2 formula is as follows: a2 – b2 = (a + b).(a – b)

## Difference of Squares Formula

The difference of two squares is calculated using the standard algebraic identity a2 – b2. For example, we are given two variables, a and b then the difference of their squares is calculated using the formula, a2 â€“ b2 = (a+b).(aâ€“b)

Basically, the difference of squares formula says that for any two algebraic variables a and b, the expression a2 â€“ b2 is equal to the product of the sum and difference of the variables. This identity is used widely to simplify complicated algebraic expressions.

## a2 – b2 Square Formula Proof

a2 – b2 identity can be proved by simplifying the RHS of the identity. The a2 – b2 formula is given as,

a2 – b2 = (a – b)(a + b)

This formula is proved as,

RHS = (a+b) (aâ€“b)

â‡’ RHS = a (aâ€“b) + b (aâ€“b)

â‡’ RHS = a2 â€“ ab + ba â€“ b2

â‡’ RHS = a2 â€“ ab + ab â€“ b2

â‡’ RHS = a2 â€“ b2

â‡’ RHS = LHS

Hence Proved.

## a2 + b2 Formula

The a2 + b2 formula is the algebraic formula that is used to find the sum of squares of two numbers. The sum of the square formula is given as,

a2 + b2 = (a + b)2 – 2ab

The a2 + b2 formula is used to solve various algebraic problems. Various other important algebraic formulas are added below,

## (a + b)2 and (a – b)2 Formula

The (a + b)2 formula is given as,

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

The (a – b)2 formula is given as,

(a – b)2 = a2 + b2 – 2ab

## a2 – b2 Identity

a2 – b2 identity is one of the algebraic identities that is used to find the difference between squares of two numbers. This identity has various applications and is given as,

a2 – b2 = (a – b).(a + b)

## Examples on a2 – b2 Formula

Example 1: Simplify x2 â€“ 16

Solution:

= x2 â€“ 16

= x2 â€“ 42

We know that, a2 â€“ b2 = (a+b) (aâ€“b)

Given,

• a = x
• b = 4

= (x + 4)(x â€“ 4)

Example 2: Simplify 9y2 â€“ 144

Solution:

= 9y2 â€“ 144

= (3y)2 â€“ (12)2

We know that, a2 â€“ b2 = (a+b)(aâ€“b)

Given,

• a = 3y
• b = 12

= (3y + 12)(3y â€“ 12)

Example 3: Simplify (3x + 2)2 â€“ (3x â€“ 2)2

Solution:

We know that,

a2 â€“ b2 = (a+b)(aâ€“b)

Given,

• a = 3x + 2
• b = 3x â€“ 2

(3x + 2)2 â€“ (3x â€“ 2)2

= (3x + 2 + 3x â€“ 2)(3x + 2 â€“ (3x â€“ 2))

= 6x(3x + 2 â€“ 3x + 2)

= 6x(4)

= 24x

Example 4: Simplify y2 â€“ 100

Solution:

= y2 â€“ 100

= y2 â€“ (10)2

We know that,

a2 â€“ b2 = (a+b)(aâ€“b)

Given,

• a = y
• b = 10

= (y + 10)(y â€“ 10)

Example 5: Evaluate (x + 6) (x â€“ 6)

Solution:

We know that,

(a+b) (aâ€“b) = a2 â€“ b2

Given,

• a = x
• b = 6

(x + 6) (x â€“ 6)

= x2 â€“ 62

= x2 â€“ 36

Example 6: Evaluate (y + 13)(y â€“ 13)

Solution:

We know that,

(a+b) (aâ€“b) = a2 â€“ b2

Given,

• a = y
• b = 13

(y + 13).(y â€“ 13)

= y2 â€“ (13)2

= y2 â€“ 169

Example 7: Evaluate (x + y + z).(x + y â€“ z)

Solution:

We know that,

(a+b) (aâ€“b) = a2 â€“ b2

Given,

• a = x + y
• b = z

(x + y + z) (x + y â€“ z)

= (x + y)2 â€“ z2

= x2 + y2 + 2xy â€“ z2

## (a2 – b2) Formula – Worksheet

Q1. Simplify 152 – 142 using a2 – b2 identity.

Q2. Simplify 112 – 72 using a2 – b2 identity.

Q3. Solve 232 – 92 using a2 – b2 identity.

Q4. Solve 92 – 72 using a2 – b2 identity.

## a2 – b2 Formula – FAQs

### 1. What is a2 âˆ’ b2?

a2 – b2 formula is the formula that is used to find the difference between two squares without actually finding the square. The a2 – b2 formula is,

a2 – b2 = (a + b)(a – b)

### 2. What is Law of a2 b2 Formula?

Law of a2 b2 formulas are,

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

### 3. What is a2 b2 Formula Used for?

a2b2 formula is used for solving various algebraic problems, they are also used for simplifying trigonometric, calculus, and integration problems.

### 4. What is a2b2 Formula?

There are two a2b2 formulas that are, a2 + b2, and a2 – b2 the expansion formula for a2b2 formulas are given as,

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

### 5. When is a2 – b2 Formula is Used?

a2 – b2 formula is used for finding the difference between squares of two numbers without actually finding the squares. This formula is also used for solving various algebraic, trigonometric, and other problems.

Previous
Next