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).
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.
Related Questions
Consider the following two statements.
Statement 1: The factorisation of x2 + 2x + 1 is (x - 1)2.
Statement 2: (a - b)2 = a2 + 2ab + b2.
Which of the following is valid?
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.
Assertion (A): For the trinomial 2x2 + 8x - 9 cannot be factorised.
Reason (R): For trinomial ax2 + bx + c to be factorised, b2 - 4ac must be a perfect square.
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).
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).
Factorise the following:
15(2x - 3)3 - 10(2x - 3)