One of the factors of (25x² – 1) + (1 + 5x)² is
(a) 5 + x
(b) 5 – x
(c) 5x – 1
(d) 10x

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Solution

$(25 x^{2} - 1) + {(1 + 5 x)}^{2} = ({(5 x)}^{2} - {(1)}^{2}) + {(1 + 5 x)}^{2} = (5 x - 1) (5 x + 1) + (1 + 5 x) (1 + 5 x) (Using the identity : a^{2} - b^{2} = (a + b) (a - b)) = (5 x + 1) (5 x - 1 + 1 + 5 x) = (5 x + 1) (10 x) Therefore, (25 x^{2} - 1) + {(1 + 5 x)}^{2} has two factors (5 x + 1) and (10 x) . Hence, the correct option is (d) .$

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Similar questions

One of the factors of $(25 x^{2} - 1) + (1 + 5 x)^{2}$ is

A) $5 + x$
B) $5 - x$
C) $5 x - 1$
D) $10 x$

(25 x^{2} - 1) + (1 + 5 x)^{2}

5 + x

5 - x

5 x - 1

10 x

One of the factors of $(25 x^{2} - 1) + (1 + 5 x)^{2}$ is

(- 25 x^{2} - 1) + (1 + 5 x)^{2}

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