Question

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

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

Answer 1

The answer is D.
$(25x^2–1)+(1+5x{)}^2$
$=25x^2-1+1+25x^2+10x$ [Using identity, $(a+b{)}^2=a^2+b^2+2ab]$
$=50x^2+10x=10x(5x+1)$
Hence, one of the factor of given polynomial is 10x.