Mathematics
Assertion (A): Factorisation of 4x2 + 9y2 is (2x - 3y)(2x + 3y).
Reason (R): a2 - b2 = (a - b)(a + b)
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
According to reason: a2 - b2 = (a - b)(a + b)
Expanding, (a - b)(a + b)
⇒ a(a + b) - b(a + b)
⇒ a2 + ab - ab - b2
⇒ a2 - b2.
Thus, (a - b)(a + b) = a2 - b2
∴ Reason (R) is true.
Given,
⇒ (2x - 3y)(2x + 3y)
⇒ 2x(2x + 3y) - 3y(2x + 3y)
⇒ (2x)2 + 6xy - 6xy - (3y)2
⇒ 4x2 - 9y2.
∴ Assertion (A) is false.
∴ Assertion (A) is false, Reason (R) is true.
Hence, option 2 is the correct option.
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Related Questions
Consider the following two statements.
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