Mathematics
Assertion (A): Factorisation of x3 - 27 is (x - 3)(x2 + 3x + 9).
Reason (R): a3 - b3 = (a - b)(a2 + ab + b2).
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Factorisation
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Answer
We know that,
a3 - b3 = (a - b)(a2 + ab + b2)
∴ Reason (R) is true.
Given,
⇒ x3 - 27
⇒ x3 - 33
⇒ (x - 3)(x2 + 3x + 32)
⇒ (x - 3)(x2 + 3x + 9).
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
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