Question

Find the factor of $(49x^2-1)+(1+7x{)}^2$.

$\left[2\right]$

Answer 1

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

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

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


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

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

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