Question

Find the product: $\left(x+7y\right)\left(7x-y\right)$

Answer 1

Simplify using the algebraic identities:

The given expression is $\left(x+7y\right)\left(7x-y\right)$.

It can be simplified as follows,

$\left(x+7y\right)\left(7x-y\right)=x\left(7x-y\right)+7y\left(7x-y\right)$ $[\because (a+b)(c-d)=a(c-d)+b(c-d\left)\right]$

$\Rightarrow \left(x+7y\right)\left(7x-y\right)=x\times 7x-x\times y+7y\times 7x-7y\times y$

$\Rightarrow \left(x+7y\right)\left(7x-y\right)=7x^{1+1}-xy+49xy-7y^{1+1}$ $\left[\because a^m\times a^n=a^{m+n}\right]$

$\Rightarrow \left(x+7y\right)\left(7x-y\right)=7x^2+48xy-7y^2$ $[\because (a-b)(a+b)=a^2-b^2]$

$\Rightarrow \left(x+7y\right)\left(7x-y\right)=7x^2-7y^2+48xy$

Hence, the product of $\left(x+7y\right)\left(7x-y\right)$ is $7x^2-7y^2+48xy$.