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

5 + x

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5 - x

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5x - 1

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10x

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Solution

The correct option is D
10x

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

= $25 x^{2} - 1 + 1 + 25 x^{2} + 10 x$ [Using identity, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ]

= $50 x^{2} + 10 x = 10 x (5 x + 1)$

Hence, one of the factors of given polynomial is $10 x$ .

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Similar questions

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

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

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

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