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# a2 b2 Formula- Proof and Questions and Answers

## a2 b2 Formula

a2 b2 Formula: One of the most fundamental algebraic formulas, the a2 b2 formula is mostly applied in mathematical calculations. The a2 b2 formula is very important for board exams as well as various competitive exams. It is always advisable to memorize these fundamental algebraic formulas so you can solve mathematical problems quickly and efficiently. Here, We will discuss the a2 b2 formula of a2+b2 and a2-b2.To gasp the a2 b2 formulas, we provide few solved examples.

## a2+b2 Formula

Let’s assume that a and b are two mathematical variables that represent two algebraic terms. The a2 + b2 formula is used to get the sum of two or more squares in an expression. The (a+b)²or (a-b)² formula can be used to obtain the a2 + b2 formula quickly. A sum of squares formula, often known as the a2 + b2 formula, can be written as follows:

## a2+b2 Formula- Proof

We are aware of this. (a +b)² = a² + b² + 2ab

a² + b² = (a +b)² – 2ab

Also we can say that (a -b)² = a² + b² – 2ab

a² + b² = (a -b)² + 2ab

The two formulas for a2+b2 are

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

### Steps for Applying the A2 + B2 Formula in math

The sum of squares formula or a2+b2 formula is applied while performing the subsequent stages.
1. First, look at the pattern of the two integers, including whether or not they are in the form of a2 + b2.
2.Write down the formula for the sum of squares for a2 + b2: (a + b)2 -2ab.
3. Simplify the sum of squares a2 + b2 formula by replacing the values of a and b.

## a2-b2 Formula

The formula a2 – b2 is frequently referred to as “the difference of squares formula.” Without calculating the two squares, the square minus b square is utilized to determine their difference.  The formula a2 – b2is applied to factorize square binomials.

The a– b2 formula is represented as: a– b= (a – b) (a + b)

## a2-b2 Formula- Proof

To demonstrate that a2 – b2 = (a – b) (a + b), we must prove LHS = RHS. Let us try to solve the following equation:

a– b= (a – b) (a + b)
Multiplying  (a – b) and (a + b) we get,
=a(a+b) -b(a + b)
=a2 + ab – ba – b2
=a2 + 0 + b2
=a2 – b2 .

Hence we can say that a– b= (a – b) (a + b)

## a2 b2  All Related Formulas

Here are some important and frequently used Algebra formulas involving squares.
• a²– b² = (a – b)(a + b)
• (a + b)²=  a²+ 2ab + b²
• a²+ b²= (a + b)²– 2ab
• (a – b)² = a²– 2ab+ b²
• (a + b + c)² = a² + b² + c²+ 2ab + 2bc + 2ca
• (a – b – c)² = a²+ b²+ c²– 2ab + 2bc – 2ca

## a2 b2 Formula- Questions and Answers

Example 1: Find the value of 9²+ 6², using the sum of a²b² formula.
Solution: Here .the value of a = 9 and b= 6 .
The formula of the sum of a²b² formula is
(a²+b²)= (a+b)²-2ab
=  (9²+2×9×6+6²)- 2×9×6 [using (a+b)² formula]
= 81 + 108 +36 -108
=81 +36 = 117
Example 2: Using the a² +b² formula, calculate the sum of 14² + 20²
Solution: Here.the value of a = 14 and b= 20 .
The formula of the sum of a²b² formula is
(a²+b²)= (a+b)²-2ab
=  (14²+2×14×20+20²)- 2×14×20 [using (a+b)² formula]
= 196 + 560+400 -560
=196 +400 = 596
Example 3 : Using a2b2 formula,Prove, 8²+ 6² = 10² .
The formula of the sum of squares or a²+ b² formula is
(a²+b²)= (a+b)²-2ab
For the proving of the given expression, we need to prove L.H.S=R.H.S
L.H.S = (a²+b²)
= (8²+6²)
=(8²+2×8×6+6²)- 2×8×6
= 64 + 96 +36 -96
= (64 +36) = 100 = 10² = R.H.S
L.H.S= R.H.S [ Proved]
Example 4: Find the value of 100²-8², using the a²-b² formula.
Solution:
The formula of the Subtraction of squares or a²- b² formula is
(a²- b²) =(a+b)(a-b)
In the given expression, a=100 ,b= 8
100²-8²= (100+8)(100-8)
= 108× 92 =9936.
Example 5: Using the a²-b² formula, calculate the value of 25²-5²
Solution: The formula of the Subtraction of squares or a²- b² formula is
(a²- b²) =(a+b)(a-b)
In the given expression, a=25 ,b= 5
25²-5²= (25+5)(25-5)
= 30× 20 =600.

## A Square Minus B Square (a2 b2) Formula- Worksheet

Here some problems based on the a2b2 formula are given below. Students are advised to solve the following problem in order to understand the applications of the a2b2 formula in a better way.

Q.Using the a²-b² formula, calculate the value of 15²-7²

Q.Simplify the expression,13²+ 6² using the a2b2 formula.

Q. Prove the a²+ b² formula using the (a+b)² formula.

Q. Using the a2b2 formula, Prove, 7²+ 9²=  10×13.

## a2 b2 Formula- FAQs

Q.What is the a2 b2 formula?
One of the most fundamental algebraic formulas, the a2 b2 formula is primarily employed in calculations. It comprises the a²+b²and a²-b² formulae.
Q. What is the a2+b2 formula?
The a² + b² Formula is a² + b² = (a +b)² – 2ab and also written as, a² + b² = (a -b)² + 2ab.
Q. What is a2- b2 formula?
The formula of the Subtraction of squares or a²- b² formula is (a²- b²) =(a+b)(a-b)
Q. How should the a2 + b2 Formula be used?
Ans. To determine whether two terms have the power of 2 or not, first look at the pattern of terms provided in the question.
If it is in the form a2 + b2, then use the sum of squares formula a2 + b2 = (a + b)2 -2ab, substituting the values of a and b.
Q.Where does the a2 b2 formula come from?
a2 + b2 is the sum of the squares of a and b.
Using the algebraic identity (a+b)² = a²+ b² + 2ab, we could derive the formula of a2 + b2.
a2 + b2 = (a + b)² -2ab is the result of substituting 2ab from both sides.
It can be written as  a²+ b² = (a – b)²+ 2ab.

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## FAQs

### What is the a2 b2 formula?

One of the most fundamental algebraic formulas, the a2 b2 formula is primarily employed in calculations. It comprises the a²+b²and a²-b² formulae.

### What is the a2+b2 formula?

The a² + b² Formula is a² + b² = (a +b)² - 2ab and also written as, a² + b² = (a -b)² + 2ab.

### What is a2- b2 formula?

The formula of the Subtraction of squares or a²- b² formula is (a²- b²) =(a+b)(a-b)

### How should the a2 + b2 Formula be used?

To determine whether two terms have the power of 2 or not, first look at the pattern of terms provided in the question.
If it is in the form a2 + b2, then use the sum of squares formula a2 + b2 = (a + b)2 -2ab, substituting the values of a and b.

### Where does the a2 b2 formula come from?

a2 + b2 is the sum of the squares of a and b.
Using the algebraic identity (a+b)² = a²+ b² + 2ab, we could derive the formula of a2 + b2.
a2 + b2 = (a + b)² -2ab is the result of substituting 2ab from both sides.
It can be written as  a²+ b² = (a - b)²+ 2ab.