Mathematics

Factorise the following:
a(b - c)(b + c) - d(c - b)

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a(b - c)(b + c) - d(c - b) = a(b - c)(b + c) - d(-1)(b - c)

= a(b - c)(b + c) + d(b - c)

= (b - c)[a(b + c) + d]

Hence, a(b - c)(b + c) - d(c - b) = (b - c)[a(b + c) + d].

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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).
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