A Square Plus B Square Formula

a square plus b square formula

a² + b² Formula

To calculate the sum of two or more squares in an expression, the a² + b² formula is used. The a² + b² formula can be easily derived using the (a+b)² or (a-b)² formula. Let us learn these along with a few solved examples in the upcoming sections.

What Is the a² + b² Formula?

The a² + b² formula is used to calculate the sum of two or more squares in an expression. Thus, a sum of squares formula or a² + b² formula can be expressed as:

a² + b² = (a +b)² – 2ab

Also, a² + b² = (a – b)² + 2ab

where, a, b = arbitrary numbers.

Let a and b be the two numbers, the squares of a and b are a² and b². The sum of the squares of a and b is a² + b². We could obtain a formula using the known algebraic identity (a+b)² = a² + b² + 2ab. On subtracting 2ab from both the sides we can conclude that a² + b² = (a +b)² – 2ab.

Similarly, we can also say that, a² + b² = (a – b)² + 2ab.

Lets understand with some solved examples

Example 1: Using sum of squares formula, find the value of 5² + 6²?

Solution:

To find : value of 5² + 6²

Given: a = 5, b = 6 

Using sum of squares Formula,

a² + b² = (a + b)² − 2ab

5² + 6² = (5 + 6)² − 2(5)(6)

= 121 − 2(30)

= 121 − 60

= 61

Answer: The value of 5² + 6² is 61.

Example 2 : Verify that the value of x² + y² is (x + y)² – 2xy using a² + b² formula.

Solution: To verify x² + y² = (x + y)² – 2xy

Let us use the a² + b² formula

a = x, b = y

Using the (a + b)² formula let us expand the initial terms.

(a + b)² = a² + b² + 2ab

Let us substitute the value of a and b as x and y

(x + y)² = x² + y² + 2xy

On subtracting 2xy from both the sides,

x² + y² = (x + y)² – 2xy