Math Formulas

What Is The Formula For a2 b2, a²+b² and a²-b²? Proof & Q/A

Formula for a2 b2, a²+b² and a²-b², we will implement. In this post we will solve proofs and question and answers.

What Is The a2 b2 Formula?

The formula a2 b2 is a quadratic equation that can also be written in the form a²+b² and a²-b². It is used to find the roots of a quadratic equation, which are the values of x that make the equation equal to zero. Questions related to this come in Class 8th, 10th, Army, NDA, AFCAT, SSC, Railway, etc exams. These questions are very easy if you know how to apply their formula. It is always advisable to memorize these basic algebra formulas so that you can find solutions to mathematical problems quickly and easily.

Also, check this: Multiplication Table 2 to 20 in Hindi & English | 2 से 20 तक पहाड़े

What Is The a2+b2 Formula?

The formula a2 + b2 is a mathematical equation that calculates the sum of the squares of two numbers. Let a and b be two mathematical variables that represent two algebraic terms. When you add the square of both algebraic terms, it will be written as a²+b². It expresses the binomial algebraic equation. The a2 b2 formula for a²+b² is explained below along with the mathematical expressions.


(a + b)² = a² + b² + 2ab [ (a + b)² can also be written as a² + b² + 2ab ]
a² + b² = (a + b)² – 2ab

So, there are two formulas related to a²+b² as explained below.

1. a² + b² = (a + b)² – 2ab
2. a² + b² = (a – b)² + 2ab

Example of a²+b² Formula with Proof

To find: a value of 52 + 62

Given: a = 5, b = 6

Using the sum of squares Formula,

a2 + b2 = (a + b)2 − 2ab

52 + 62 = (5 + 6)2 − 2(5)(6)

= 121 − 2(30)

= 121 − 60

= 61

What Is The a²-b² Formula?

Considering that a and b are two algebraic variables, let’s consider them together. By subtracting the squares of both algebraic terms, you get a2-b2. An algebraic equation with binomial coefficients is represented by this expression. Below are the mathematical expressions for the a2 b2 formula.

Based on the a2-b2 formula, a2-b2 is made up of the factors (a+b) and (a-b). It is possible to deduce the a2-b2 formula geometrically.

Using a small box of side b to subtract from a large square of side a, a new geometric shape with area a2-b2 is produced. Subtracting a shape from another is found to have an area of a2-b2, while transforming that shape into a rectangle with the size of (a+b) and (a-b) is found to have an area of (a+b). Hence, the rectangle’s area is equal to the square’s area. Then, we will be able to get that

a²-b² = (a+b) (a−b)

Example of a²-b² Formula with Proof

Question: With the help of the sum of squares formula, calculate the value of (17)² – (16)².

Solution: Given that the value of a = 17, b = 16
By using the subtraction of squares formula,

a² – b² = (a + b) (a – b)

17² – 16² = (16 + 17) (16 – 17) = 289 – 256 = 33

a2 b2 Formula- Questions and Answers

Question: With the help of the subtraction of squares formula, find the value of the given expression (13 + 6) (13 – 6).

Solution: Given that the value of a = 13, b = 6

By using the subtraction of squares formula,

a² – b² = (a + b) (a – b)

13² – 6² = (13 + 6) (13 – 6)

(13 + 6) (13 – 6) = 169 – 36 = 133

Proof of the A2 + B2 Formula | Easy Way

a2 – b2=(a+b)(a-b)

a2 – b2 is the algebraic expression for the difference between two square quantities. By factoring, it can be expressed as the product of two special binomials (a+b) and (a-b). Mathematically, factorization can be used to determine the factoring form of a difference of squares.

  1. Using the algebraic form, find the difference between squares

Mathematics represents two terms by the difference of squares of their squares a2 and b2.

  1. Factoring adjustment of a small amount

The difference between the two squares needs to be factored in with a small adjustment. You can accomplish this by adding and subtracting ab from the right-hand side of the algebraic equation.

a2-b2 = a2-b2-ab+ab
a2-b2 = a2-ab+ab-b2

  1. Calculate the factorization of the algebraic expression a2-b2 = a2-ab+ab-b2

By factorizing the right side of the equation, the right-hand side will be able to be factored. Two of the first three terms have the same factor a. Two of the last three terms have the same factor b. They can therefore be factored in.

a2-b2 = a(a-b) + b(a-b)

As you can see, (a-b) is a common factor in both terms on the right.

a2-b2 = (a-b)(a+b)
=> a2-b2 = (a+b)(a-b)

FAQs: a2 b2 Formula

Q:1 What is the a2 b2 Formula?

Ans: Formula a² + b² is a² + b² = (a +b)² – 2ab and also written as, a² + b² = (a -b)² + 2ab

Q:2 What is the a2-b2 Formula?

Ans: The formula a2-b2 is a²- b² formula is (a²- b²) =(a+b)(a-b)

Q:3 How is the a2 + b2 formula used?

Ans: Check the pattern, If it’s in the form a2 + b2, use the sum of squares formula a2 + b2 = (a + b)2 -2ab, substituting the values for a and b.

Q:4 Where did the a2 b2 formula come from?

Ans: The sum of the squares of a and b is a2 + b2. The formula for a2 + b2 can be derived using the algebraic identity (a+b)2 = a2+ b2 + 2ab.By substituting 2ab from both sides, a2 + b2 = (a + b)2 -2ab is obtained.As a2+b2 = (a – b)2+ 2ab, this can be written as a2+b2.

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