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

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(C) Given expression: $(25 x^{2}-1)+(1+5 x)^{2}$Using the identity $a^{2}-b^{2}=(a-b)(a+b)$,we can write $(25 x^{2}-1)$ as $(5 x)^{2}-1^{2}=(5 x-1)(5

Vedclass · Accepted Answer

$10x$

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(C) Given expression: $(25 x^{2}-1)+(1+5 x)^{2}$Using the identity $a^{2}-b^{2}=(a-b)(a+b)$,we can write $(25 x^{2}-1)$ as $(5 x)^{2}-1^{2}=(5 x-1)(5 x+1)$.Substituting this into the expression:$(5 x-1)(5 x+1)+(5 x+1)^{2}$Taking $(5 x+1)$ as a common factor:$(5 x+1) 	imes [(5 x-1)+(5 x+1)]$Simplifying the terms inside the square bracket:$(5 x+1) 	imes (5 x-1+5 x+1) = (5 x+1)(10 x)$Thus,the factors are $10 x$ and $(5 x+1)$.Therefore,$(c)$ is the correct answer.

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

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