# 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} = (a^{2 }± 2ab + b^{2})

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} = (a^{2 }+ 2ab + b^{2})

Put the values,

(6x + 4y)^{2} = ((6x)^{2 }+ 2 × 6x × 4y + (4y)^{2})

(6x + 4y)^{2}= (36x^{2 }+ 48x + 16y^{2})

**Answer: **The the square of 6x^{ }+ 4y is (36x^{2 }+ 48x + 16y^{2}).

**Example 2:**

### Find if x^{2} + 25 - 10x is perfect square or not.

**Solution:**

To find: x^{2} + 25 - 10x is perfect square or not.

Rearranging the terms:

x^{2} + 25 - 10x = x^{2} + 5 × 5 - 2 × 5 × x = x^{2} - 2 × 5 × x + 5 × 5

Using the perfect square formula.

(a - b)^{2} = (a^{2 }- 2ab + b^{2})

Comparing the values,

x^{2} - 2 × 5 × x + 5 × 5 = (x - 5)^{2}

**Answer: **x^{2} + 25 - 10x is perfect square.

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