Difference of Squares Formula
In mathematics, the difference of squares formula is one of e primary algebraic formulas in which the difference of two squared values is equal to the product of sum of the values and the difference of the values. This type of formula helps us to convert a complex equation of difference of squares in a few quick steps. Let us learn about the difference of squares formula with a few solved examples at the end.
What Is the Difference of Squares Formula?
The difference of squares is nothing but the subtraction of the square of one number from another number. The difference of squares formula for two values a and b can be given as follows.
a2-b2 = (a+b)(a-b)
where,
- a is the first variable
- b is the second variable
Let us explore more about the subtraction of squares formula with the help of solved examples.
Solved Examples Using Difference of Squares Formula
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Example 1: There are 12 boxes of chocolates in a shop and each box contains 12 chocolates. If a few of these chocolates were transferred into 10 boxes and each box could accommodate only 10 chocolates. Find out how many chocolates are left using the difference of squares formula?
Solution:
To find: Remaining number of chocolates.
Total number of chocolates boxes = 12 (given)
Each box contains =12 chocolates
So, total no. of chocolates in 12 boxes =\(12 x12\) = \(12^2\)
Total no. of chocolate transferred in 10 boxes = \(10 x 10\) = \(10^2\)
Using difference of squares formula,
Remaining number of chocolates = (Chocolates in 12 boxes - Chocolates in 10 boxes)
= \((12^2-10^2)=(12+10)(12-10)\)
= 44 chocolates
Answer: 44 chocolates will be leftover.
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Example 2: What is the value of \({8^2} − {7^2}\)?
Solution:
To find: Difference between the squares of two numbers.
First number = 8
The second number = 7
Using the difference of squares formula,
Difference between the squares of two numbers. = (Square of the first number - Square of the second number)
= \({8^2} − {7^2}=(8+7)(8-7)\)
= 15
Answer: The difference between the squares of two numbers 8 and 7 is 15.
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