Evaluate the Difference of Two Squares

Learn how to use the formula to evaluate the difference of two squares.

We know, the formula of difference of two squares a2 - b2 = (a + b) (a – b).

Examples to evaluate the difference of two squares:

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

(i) (502)2 - (498)2

Solution:

(502)2 -(498)2

Since the given algebraic expression is in the form of a2 – b2 so, here we will directly apply the formula a2 - b2 = (a + b) (a – b) to evaluate the difference of two squares.

Here, a = 502 and b = 498

= (502 + 498) (502 - 498)

= (1000) (4), [simplifying]

= 4000.

(ii) (601)2 - (599)2

Solution:

(601)2 - (599)2

Since the given algebraic expression is in the form of a2 – b2 so, here we will directly apply the formula a2 - b2 = (a + b) (a – b) to evaluate the difference of two squares.

Here, a = 601 and b = 599

= (601 + 599) (601 - 599)

= (1200) (2), [simplifying]

= 2400.

(iii) (8.6)2 - (1.4)2

Solution:

(8.6)2 - (1.4)2

Since the given algebraic expression is in the form of a2 – b2 so, here we will directly apply the formula a2 - b2 = (a + b) (a – b) to evaluate the difference of two squares.

Here, a = 8.6 and b = 1.4

= (8.6 + 1.4) (8.6 - 1.4)

= (10) (7.2), [simplifying]

= 72

(iv) (99.8)2 - (0.2)2

Solution:

(99.8)2 - (0.2)2

Since the given algebraic expression is in the form of a2 – b2 so, here we will directly apply the formula a2 - b2 = (a + b) (a – b) to evaluate the difference of two squares.

Here, a = 99.8 and b = 0.2

= (99.8 + 0.2) (99.8 – 0.2)

= (100) (99.6), [simplifying]

= 9960

(v) (8.2)2 - (1.8)2

Solution:

(8.2)2 - (1.8)2

Since the given algebraic expression is in the form of a2 – b2 so, here we will directly apply the formula of a2 - b2 = (a + b) (a – b)

Here, a = 8.2 and b = 1.8

= (8.2 + 1.8) (8.2 – 1.8)

= (10.0) (6.4), [simplifying]

= 64

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