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)

perfect square formula

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Examples on Perfect Square Formula

Let us consider few illustrations based on the (a+b)^2 formula in this solved examples section.

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)

Answer: The 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

Answer: 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

Answer: (7x - 2y)2 = 49x2 - 28xy + 4y2.

FAQs on Perfect Square Formula

What Is the Expansion of Perfect Square Formula?

The expansion of the perfect square formula is expressed as (a + b)2  =  a2 + 2ab + b2.

What Is Are the Two Perfect Squares Formula in Algebra?

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.

How To Represent the Perfect Square Formula?

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.

How To Use the Perfect Square Formula?

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.
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