One of the factors of $(25 x^{2} - 1) + {(1 + 5 x)}^{2}$ is
(a) 5 + x
(b) 5 – x
(c) 5x – 1
(d) 10x

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Solution

$(25 x^{2} - 1) + {(1 + 5 x)}^{2} = (5 x - 1) (5 x + 1) + {(1 + 5 x)}^{2} = (5 x + 1) [(5 x - 1) + (1 + 5 x)] = (5 x + 1) (10 x)$
So, the factors of $(25 x^{2} - 1) + {(1 + 5 x)}^{2}$ are (5x + 1) and 10x
Hence, the correct answer is option (d).

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

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

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