Perfect Square Formula

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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 = (a± 2ab + b2)

or

a dn b cube

 

 

 

 

 

 

 

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= (36x+ 48x + 16y2)

Answer: The the square of 6x + 4y is (36x+ 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.