Examples on Perfect Square Formula

Example 1: Find square of (2x + y) using perfect formula

Solution: 

Given (2x + y)²

Using perfect square formula

(a + b)² = a² + 2ab + b²

a = 2x and b = y

Put the values

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

(2x + y)² = (4x² + 4xy + y²)

Square of (2x + y) is 4x² + 4xy + y².

Example 2: Simplify (5x+2y)² using the perfect square formula.

Solution:      

Using perfect square formula

(a + b)² = a² + 2ab + b²

a = 5x and b = 2y

Put the values

(5x + 2y)² = ((5x)² + 2 × (5x) × (2y) + (2y)²)                                    

So, (5x + 2y)² = 25x² + 20xy + 4y²

Example 3: Find if x² + 4y² + 4xy is perfect square or not.

Solution:   

Given x² + 4y² + 4xy

Now rearranging the given expression;

x² + 4xy + 4y²

On expanding the above equation we get

((x) × (x)) + 2 × (x) × (2y) + ((2y) × (2y))

On comparing with perfect square formula, we get

(a + b)²= a² + 2ab + b²

On comparing values we get

a = x and b = 2y

So, x² + 4y² + 4xy = (x + 2y)²

Hence, x² + 4y² + 4xy is perfect square.

Example 4: Evaluate: (99)²

Solution:   

So, it can also be written as:

(100 – 1)²

Using perfect square formula:

(a – b)² = a² + 2ab + b²

a = 100 and b = 1

(100 – 1)² = ((100)² – 2 × (100) × (1) + (1)²

(100 – 1)² = (10000 – 200 + 1)

(100 – 1)² = (10001 – 200)

(100 – 1)² = 9801

So (99)² = 9801

Example 5: Find if x² + 4 – 4x is perfect square or not.

Solution:   

Given x² + 4 – 4x

Rearranging the above expression;

x² – 4x + 4    

On expanding, we get

((x) × (x)) – 2 × (x) × (2) + ((2) × (2))

On comparing with perfect square formula

(a – b)² = a² – 2ab + b²

On comparing values we get

a = x and b = 2

So, x² + 4 – 4x = (x – 2)²

Hence, x² + 4 – 4x is a perfect square

Perfect Square Formula: A polynomial or number which when multiplied by itself is called a perfect square. The perfect square is calculated by two algebraic expressions that include: (a + b)² = a² + 2ab + b² and (a – b)² = a² – 2ab + b².

In this article, we have covered the perfect square definition, how to identify perfect square, perfect square formulas, and other related topics in detail.