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 a
^{2} - b
^{2} = (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 a
^{2} – b
^{2} so, here we will directly apply the formula a
^{2} - b
^{2} = (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 a
^{2} – b
^{2} so, here we will directly apply the formula a
^{2} - b
^{2} = (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 a
^{2} – b
^{2} so, here we will directly apply the formula a
^{2} - b
^{2} = (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 a
^{2} – b
^{2} so, here we will directly apply the formula a
^{2} - b
^{2} = (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 a
^{2} – b
^{2} so, here we will directly apply the formula of a
^{2} - b
^{2} = (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
8th Grade Math Practice
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