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## Solved Problems to Evaluate the Difference of Two Squares

Use the formula of the difference of two squares to evaluate the following algebraic expressions:

(i) (202)2 – (123)2

Solution:
Given expression is (202)2 – (123)2
The above equation (202)2 – (123)2 is in the form of a2 – b2.
(202)2 – (123)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 202 and b = 123
(202 + 123) (202 – 123)
(325) (79)
25675

The final answer is 25675.

(ii) (600)2 – (598)2

Solution:
Given expression is (600)2 – (598)2
The above equation (600)2 – (598)2 is in the form of a2 – b2.
(600)2 – (598)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 600 and b = 598
(600 + 598) (600 – 598)
(1198) (2)
2396

The final answer is 2396.

(iii) (4.2)2 – (2.1)2

Solution:
Given expression is (4.2)2 – (2.1)2
The above equation (4.2)2 – (2.1)2 is in the form of a2 – b2.
(4.2)2 – (2.1)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 4.2 and b = 2.1
(4.2 + 2.1) (4.2 – 2.1)
(6.3) (2.1)
13.23

The final answer is 13.23.

(iv) (97.8)2 – (0.4)2

Solution:
Given expression is (97.8)2 – (0.4)2
The above equation (97.8)2 – (0.4)2 is in the form of a2 – b2.
(97.8)2 – (0.4)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 97.8 and b = 0.4
(97.8 + 0.4) (97.8 – 0.4)
(98.2) (97.4)
9564.68

The final answer is 9564.68.

(v) (8.4)2 – (1.8)2

Solution:
Given expression is (8.4)2 – (1.8)2
The above equation (8.4)2 – (1.8)2 is in the form of a2 – b2.
(8.4)2 – (1.8)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 8.4 and b = 1.8
(8.4 + 1.8) (8.4 – 1.8)
(10.2) (6.6)
67.32

The final answer is 67.32.