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Question
a2 – b2 is equal to ______.
Options
(a – b)2
(a – b)(a – b)
(a + b)(a – b)
(a + b)(a + b)
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Solution
a2 – b2 is equal to (a + b)(a – b).
Explanation:
a. (a – b)2 = a2 – 2ab + b2
b. (a – b)(a – b) = (a – b)2 = a2 – 2ab + b2
c. (a + b)(a – b) = a(a – b) + b(a – b) + b(a – b)
= a2 – ab + ba – b2 ...[∵ ab = ba]
= a2 – b2
d. (a + b)(a + b) = (a + b)2 = a2 + 2ab + b2
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