a2 – b2 Formula

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 – b² = (a+b).(a–b)

Basically, the difference of squares formula says that for any two algebraic variables a and b, the expression a² – 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) (a–b)

⇒ RHS = a (a–b) + b (a–b)

⇒ RHS = a² – ab + ba – b²

⇒ RHS = a² – ab + ab – b²

⇒ RHS = a² – b²

⇒ 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)

Read More,

• Algebra Formula
• Basic Maths Formula
• Algebric Expression

Examples on a² – b² Formula

Example 1: Simplify x² – 16

Solution:

= x² – 16

= x² – 4²

We know that, a² – b² = (a+b) (a–b)

Given,

• a = x
• b = 4

= (x + 4)(x – 4)

Example 2: Simplify 9y² – 144

Solution:

= 9y² – 144

= (3y)² – (12)²

We know that, a² – b² = (a+b)(a–b)

Given,

• a = 3y
• b = 12

= (3y + 12)(3y – 12)

Example 3: Simplify (3x + 2)² – (3x – 2)²

Solution:

We know that,

a² – b² = (a+b)(a–b)

Given,

• a = 3x + 2
• b = 3x – 2

(3x + 2)² – (3x – 2)²

= (3x + 2 + 3x – 2)(3x + 2 – (3x – 2))

= 6x(3x + 2 – 3x + 2)

= 6x(4)

= 24x

Example 4: Simplify y² – 100

Solution:

= y² – 100

= y² – (10)²

We know that,

a² – b² = (a+b)(a–b)

Given,

• a = y
• b = 10

= (y + 10)(y – 10)

Example 5: Evaluate (x + 6) (x – 6)

Solution:

We know that,

(a+b) (a–b) = a² – b²

Given,

• a = x
• b = 6

(x + 6) (x – 6)

= x² – 6²

= x² – 36

Example 6: Evaluate (y + 13)(y – 13)

Solution:

We know that,

(a+b) (a–b) = a² – b²

Given,

• a = y
• b = 13

(y + 13).(y – 13)

= y² – (13)²

= y² – 169

Example 7: Evaluate (x + y + z).(x + y – z)

Solution:

We know that,

(a+b) (a–b) = a² – b²

Given,

• a = x + y
• b = z

(x + y + z) (x + y – z)

= (x + y)² – z²

= x² + y² + 2xy – 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 − 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.