Mathematics
Assertion(A): One of the factors of (5x + 1)2 + (25x2 - 1) is 2x.
Reason(R): (a + b)2 = (a + b)(a + b) and a2 - b2 = (a + b)(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
Factorisation
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Answer
Given,
⇒ (5x + 1)2 + (25x2 - 1)
⇒ (5x + 1)2 + (5x)2 - (1)2
⇒ (5x + 1)2 + (5x + 1)(5x - 1)
⇒ (5x + 1)[(5x + 1) + (5x - 1)]
⇒ (5x + 1)(10x)
⇒ 2x(5)(5x + 1).
Assertion (A) is true.
⇒ (a + b)2 can be written as (a + b)(a + b)
By identity,
a2 - b2 = (a + b)(a - b)
Reason (R) is true.
Thus, both A and R are true.
Hence, option 3 is correct option.
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7 − 12m − 4m2 =
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(1 + 2m)(7 + 2m)
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Factorization of p2 − 2p − (q + 1)(q − 1) is:
(p + q − 1)(p − q + 1)
(p − q + 1)(p − q − 1)
(p + q − 1)(p − q − 1)
(p + q + 1)(p − q)
Assertion(A): can be factorized as
Reason(R): x3 - y3 = (x - y)(x2 + xy + y2).
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
One of the factors of (x2 - 4x)(x2 - 4x - 1) - 20 is :
x - 1
x - 2
x - 4
x + 5