What Are The Perfect Squares

Perfect Foursquare Formula

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

What is the Perfect Square Formula?

We apply the perfect square formula when nosotros take to calculate the square of any binomial. It calculates the foursquare of sum or difference of 2 terms or can be used in factorization. The perfect square formula is:

(a ± b)² = (a²± 2ab + b^two)

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Examples on Perfect Square Formula

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

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

Solution:

To find: Foursquare of 6x+ 4y,

Using the perfect square formula.

(a + b)² = (a^two+ 2ab + b^two)

Put the values,

(6x + 4y)² = ((6x)²+ 2 × 6x × 4y + (4y)ⁱⁱ)

(6x + 4y)²= (36x²+ 48x + 16y²)

Answer: The the square of 6x+ 4y is (36x^two+ 48x + 16y^two).

Example 2: Using the perfect square formula, find if x² + 25 - 10x is perfect foursquare or not.

Solution:

To find: 10² + 25 - 10x is perfect square or not.
Rearranging the terms:
x² + 25 - 10x = x² + 5 × v - 2 × 5 × x = x^two - 2 × v × ten + 5 × 5
Using the perfect square formula.
(a - b)² = (aⁱⁱ- 2ab + bⁱⁱ)
Comparing the values,
xⁱⁱ - ii × 5 × x + 5 × 5 = (x - 5)²

Answer: x² + 25 - 10x is perfect foursquare.

Case iii: Simplify the following using the perfect square formula.

(7x - 2y)^two

Solution:

a = 7x and b = 2y
Using perfect square formula (a - b)² = a² - 2ab + b^two
(7x)² - two(7x)(2y) + (2y)²
49xⁱⁱ - 28xy + 4y²

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

FAQs on Perfect Foursquare Formula

What Is the Expansion of Perfect Foursquare Formula?

The expansion of the perfect square formula is expressed equally (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)^two and (a - b)^two. These 2 can be read every bit a plus b whole foursquare or a minus b whole foursquare. These ii perfect squares formulas are expressed as (a + b)² = a^two+ 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 equally (a + b)² = a²+ 2ab + bⁱⁱ.

How To Utilize the Perfect Square Formula?

The post-obit steps are followed while using the perfect square formula.

Firstly observe the pattern of the numbers whether the numbers have whole ^2 equally 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)ⁱⁱ formula and simplify.