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  • One of the factors of \left ( 25x^{2}-1 \right )+\left ( 1+5x \right )^{2} is (A) 5+x (B) 5-x (C) 5x-1 (D) 10x

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

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

Answers (1)

(D) 10x

Solution

Given,

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

We know that,

(5x+1)^{2}=(5x)^{2}+2\times(5x)\times 1+1                     \left \{using\; (a+b)^{2}=a^{2}+b^{2}+2ab \right \}

Now, using the above

\left ( 25x^{2}-1 \right )+\left ( 1+5x \right )^{2}=25x^{2}-1+1^{2}+(5x)^{2}+2\times 1 \times 5x=0\\ 25x^{2}-1+1+25x^{2}+10x=0\\ 50x^{2}+10x=0\\ 10x(5x+1)=0\\  

The factors of \left ( 25x^{2}-1 \right )+\left ( 1+5x \right )^{2} are 10x and (5x+1)

Hence in the above option, (D) is correct.

Posted by

infoexpert24

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