Table of Contents

**Perfect Square Formula**

**Introduction to Perfect Square Formula **

The perfect square formula is used to find the square of the addition or subtraction of two terms, (a ± b)2 and is known as the perfect square formula. Let’s learn more about the perfect square formula in detail in the following section.

**What is the Perfect Square Formula?**

We apply the perfect square formula when we have to calculate the square of any binomial. It calculates the square of sum or difference of two terms or can be used in factorization. The perfect square formula is:

(a ± b)2 = (a2 ± 2ab + b2)

**Solved Examples on Perfect Square Formula**

**Example1: **Find the square of 6x + 4y using the perfect formulas.

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)

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

**Example 2:** Using the perfect square formula, 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

Thus, x2 + 25 – 10x is perfect square.

**Example 3:** Simplify the following using the perfect square formula.

(7x – 2y)2

Solution:

a = 7x and b = 2y

Using perfect square formula (a – b)2 = a2 – 2ab + b2

(7x)2 – 2(7x)(2y) + (2y)2

49x2 – 28xy + 4y2

**Frequently Asked Questions on Perfect Square Formula**

1: What Is the Expansion of Perfect Square Formula?

Answer: The expansion of the perfect square formula is expressed as

(a + b)2 = a2 + 2ab + b2.

2: What Is Are the Two Perfect Squares Formula in Algebra?

Answer: The two perfect squares formula in algebra are (a + b)2 and (a – b)2. These two can be read as a plus b whole square or a minus b whole square.

These two perfect squares formulas are expressed as (a + b)2 = a2 + 2ab + b2.

3: How to Represent the Perfect Square Formula?

Answer: The perfect square formula is represented in form of two terms such as (a + b)2 . The expansion of the perfect square formula is expressed as

(a + b)2 = a2 + 2ab + b2.

4: How to Use the Perfect Square Formula?

Answer: The following steps are followed while using the perfect square formula.

Firstly, observe the pattern of the numbers whether the numbers have whole ^2 as power or not.

Write down the perfect formula according to the operation present in the question (a + b)2

(a + b)2 = a2 + 2ab + b2

Substitute the value of a and b in the perfect square (a + b)2 formula and simplify.

5: How many Perfect Squares are between 1 and 100?

Answer: There are eight perfect squares between 1 and 100 (i.e., excluding 1 and 100).

They are 4, 9, 16, 25, 36, 49, 64 and 81.

However, there are ten perfect squares from 1 to 10. They are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.

6: How many Perfect Squares are between 1 and 1000?

Answer: There are 30 perfect squares between 1 and 1000. They are 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961.

7: Is 216 a perfect square?

Answer: A number is a perfect square or a square number if its square root is an integer, which means it is an integer’s product with itself. As we know, the square root of 216 is approximately equal to 14.697. Here, the square root of 216 is not an integer. Hence, it is clear that 216 is not a perfect square number.

8: What is a Perfect Square?

Answer: A perfect square is a number that is the second exponent of an integer. For example, let us take any integer, ‘a’. The perfect square will be a × a, or a2.

9: How Can you Tell if a Number is a Perfect Square?

Answer: A number is considered to be a perfect square if it can be written as a square of an integer. For example, 9 is a perfect square because 3 × 3 = 32 = 9. However, 21 is not a perfect square, because there is no whole number that can be squared to give 21 as the product.