Question

Which of the following is a factor of $(49x^2-1)+(1+7x{)}^2$?

• A. $1+7x$
• B. $49x$
• C. $1-7x$
• D. $x+1$

Answer 1

The correct option is A

$1+7x$

$(49x^2-1)+(1+7x{)}^2=(49x^2-1)+(1+7x\left)\right(1+7x)$

$=(7x-1)(7x+1)+(1+7x)(1+7x)$

[Since $49x^2-1=(7x+1)(7x-1)$]

$=(1+7x)(7x-1+1+7x)$ [Taking $(1+7x)$ as common]

$=(1+7x)\left(14x\right)$

Hence, $(1+7x)$ is a factor of $(49x^2-1)+(1+7x{)}^2$.