The difference between two squares means a square number is subtracted from another squared number. You can find the difference between the two squares using the factorization method. Students can get the definition for the difference of the squares, formula, and detailed steps to calculate it in the following sections. The solved example questions provided below are helpful for a better understanding of the concept.
Also, Refer:
Difference of the Squares – Meaning
The difference of the squares is a number which means we need the square of the second number should be subtracted from the square of the first number. We have simple tricks and formulas to calculate the difference between two square numbers those are provided below.
When the square numbers are consecutive numbers, the simple trick used to find their difference is just to add those two consecutive numbers. And the formula to calculate the difference of two squares is a² – b² = (a + b)(a – b). Here a and b are two different numbers that are to be squared.
How to find the Difference of the Squares?
Have a look at the easy steps provided below to solve the difference of the squares manually and easily.
- Find the squares of the first, second numbers.
- Subtract the square of the second number from the first number.
- The difference is the result.
(Or)
- Calculate the sum of two numbers that are to be squared.
- Also, calculate the difference between the two numbers.
- Multiply the results obtained from the above two steps to get the final difference.
Difference of the Squares Examples
Question 1:
Solve the following:
(i) 88² – 87²
(ii) 156² – 155²
(iii) 12² – 11²
Solution:
(i) Given that,
88² – 87²
The difference of the squares of two consecutive numbers is equal to the sum of two numbers.
88² – 87² = 88 x 88 – 87 x 87
= 88 + 87
= 175
Therefore, 88² – 87² = 175
(ii) Given that,
156² – 155²
The difference of the squares of two consecutive numbers is equal to the sum of two numbers.
156² – 155² = 156 x 156 – 155 x 155
= 156 + 155
= 311
Therefore, 156² – 155² = 311
(iii) Given that,
12² – 11²
The difference of the squares of two consecutive numbers is equal to the sum of two numbers.
12² – 11² = 12 x 12 – 11 x 11
= 12 + 11
= 23
Therefore, 12² – 11² = 23
Question 2:
Find the difference of the two squares
(i) 78² – 15²
(ii) 89² – 56²
(iii) 159² – 121²
Solution:
(i) Given that,
78² – 15²
We know that, a² – b² = (a + b)(a – b)
Here, a = 78, b = 15
78² – 15² = (78 + 15) (78 – 15)
= 93 x 63
= 5859
Therefore, 78² – 15² = 5859
(ii) Given that,
89² – 56²
We know that, a² – b² = (a + b)(a – b)
Here, a = 89, b = 56
89² – 56² = (89 + 56) (89 – 56)
= 145 x 33
= 4785
Therefore, 89² – 56² = 4785
(iii) Given that,
159² – 121²
We know that, a² – b² = (a + b)(a – b)
Here, a = 159, b = 121
159² – 121² = (159 + 121) (159 – 121)
= 280 x 38
= 10640
Therefore, 159² – 121² = 10640
Question 3:
(i) 72 x 72 – 54 x 54
(ii) 756² – 755²
(iii) 81² – 14²
Solution:
(i) Given that,
72 x 72 – 54 x 54 = 72² – 54²
We know that, a² – b² = (a + b)(a – b)
Here, a = 72, b = 54
72² – 54² = (72 + 54) (72 – 54)
= 126 x 18
= 2268
Therefore, 72 x 72 – 54 x 54 = 2268
(ii) Given that,
756² – 755²
The difference of the squares of two consecutive numbers is equal to the sum of two numbers.
756² – 755² = 756 x 756 – 755 x 755
= 756 + 755
= 1511
Therefore, 756² – 755² = 1511
(iii) Given that,
81² – 14²
So, 81² = 6561, 14² = 196
81² – 14² = 6561 – 196
= 63651
Therefore, 81² – 14² = 63651
FAQs on Difference of the Squares
1. What is the purpose of the difference of squares?
The difference of two squares is a theorem that explains if a binomial equation is written as the product of two binomials then it shows the sum of square roots and the difference of the square roots.
2. What is the form of two squares identity?
The difference of two squares identity is a² – b² = (a + b)(a – b). Here a and b are two different numbers that are to be squared. The difference between two squares can be defined as the product of the sum and difference of these numbers.
3. How do you find the difference of squares of two consecutive numbers?
The difference of squares of two consecutive natural or whole numbers can be defined as the sum of the consecutive numbers.