Mathematics
Statement 1: Cube of a binomial : (a - b)3 = a3 + 3a2b - 3ab2 - b3
Statement 2: (a - b)2 - (a + b)2 = 4ab.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
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Answer
Cube of a binomial:
(a - b)3 = a3 - b3 - 3ab(a - b)
= a3 - b3 - 3a2b + 3ab2
= a3 - 3a2b + 3ab2 - b3
So, statement 1 is false.
Solving,
(a - b)2 - (a + b)2
= [a2 - 2ab + b2] - [a2 + 2ab + b2]
= a2 - 2ab + b2 - a2 - 2ab - b2
= -4ab.
So, statement 2 is false.
Hence, Option 2 is the correct option.
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