Mathematics
Assertion (A): (1 - 3x)3 can be expanded as 1 - 27x3 - 9x - 27x2.
Reason (R): (a - b)3 = a3 - b3 - 3ab(a - b)
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Expansions
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Answer
Using identity,
(a - b)3 = a3 - b3 - 3ab(a - b)
So, reason (R) is true.
⇒ (1 - 3x)3 = 13 - (3x)3 - 3 × 1 × 3x (1 - 3x)
⇒ (1 - 3x)3 = 1 - 27x3 - 9x(1 - 3x)
⇒ (1 - 3x)3 = 1 - 27x3 - 9x + 27x2
So, assertion (A) is false.
Hence, Option 2 is the correct option.
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