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a2 + b2 is Equal to – a2+b2 Formula, Examples, Derivation
By BYJU'S Exam Prep
Updated on: September 25th, 2023
a2 + b2 is equal to (a + b)² – 2ab. The equation (a + b)2 = a2 + 2ab + b2 was used to derive the formula. Factorization is the process of representing an algebraic expression as the sum of two or more other expressions in order to arrive at the a2 + b2 formula. To factorise an expression, it is written as a product of its factors which may be numbers, algebraic variables, or algebraic expressions.
On factorising the expression (a + b)2 = a2 + 2ab + b2 we can obtain the formula of a2 + b2. The factorisation is done by using the distributive law property.
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a2 + b2 Formula
The derivation of the formula has been illustrated below:
- We know that the a2+b2 formula has been derived from (a + b)2 = a2 + 2ab + b2.
- Now, we will solve the above equation.
- In this equation, (a + b)2 = a2 + 2ab + b2 we will place 2ab from right hand side to left and side.
- Then the equation will be (a + b)2 – 2ab = a2 + b2.
- Hence, a2 + b2 = (a + b)² – 2ab.
a2 + b2 Formula Examples
The formula a2 + b2 represents the sum of squares of two numbers. Here are a few examples that demonstrate the application of this formula:
Example 1: Let’s consider two numbers, a = 3 and b = 4.
Substituting the values of a & b in a2 + b2 formula:
a2 + b2 = (a + b)² – 2ab
(3 + 4)2 – 2 x 3 x 4
49 – 24 = 25
So, the sum of squares of 3 and 4 is 25.
Example 2: Let’s take a negative number, a = -2, and a positive number, b = 3.
Using the formula a2 + b2, we have:
(-2 + 3)2 – 2 x (-2) x (3)
1 + 12 = 13.
Hence, the sum of squares of -2 and 3 is 13.
Summary:
What is a2 + b2 Formula?
The formula of a2 + b2 is equal to (a + b)² – 2ab. The other identities related to a2 b2 formula are (a + b) (a – b) = a2 – b2, (a – b)2 = a2 – 2ab + b2, (x + a) (x + b) = x2 + (a + b) x + ab.
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