Perfect Square Formula

The perfect square formula used to find the square of the addition or subtraction of two polynomials, (a ± b)² and is known as the perfect square formula.

Let's learn more about the sum of the perfect square formula with a few solved examples.

What is the Perfect Square Formula?

The perfect square formula is:

(a ± b)² = (a² ± 2ab + b²)

or

 

 

 

 

 

 

 

Solved Examples Using Perfect Square Formula

Example1: Find the square of 6x + 4y.

Solution: 

To find: Square of 6x + 4y,

Using the perfect square formula.

(a + b)² = (a² + 2ab + b²)

Put the values,

(6x + 4y)² = ((6x)² + 2 × 6x × 4y + (4y)²)

(6x + 4y)²= (36x² + 48x + 16y²)

Answer: The the square of 6x + 4y is (36x² + 48x + 16y²).

 

Example 2:

Find if x² + 25 - 10x is perfect square or not.

Solution:

To find: x² + 25 - 10x is perfect square or not. 

Rearranging the terms:

x² + 25 - 10x = x² + 5 × 5 - 2 × 5 × x = x²  - 2 × 5 × x + 5 × 5

Using the perfect square formula.

(a - b)² = (a² - 2ab + b²)

Comparing the values,

x²  - 2 × 5 × x + 5 × 5 = (x - 5)²

Answer: x² + 25 - 10x is perfect square.