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# Find the result after multiplication of $\left( x+7y \right)$ and $\left( 7x-y \right)$ .(a) $7{{x}^{2}}+48xy-7{{y}^{2}}$(b) $7{{x}^{2}}+48xy+7{{y}^{2}}$(c) $7{{x}^{2}}-48xy-7{{y}^{2}}$(d) $-7{{x}^{2}}-48xy+7{{y}^{2}}$  Verified
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Hint: For solving this question we will directly apply one formula and do the multiplication of the corresponding terms with each other and then solve for the correct answer.

We have to find the result of $\left( x+7y \right)\times \left( 7x-y \right)$ . Where $x$ and $y$ are variables.
$\left( a+b \right)\times \left( c+d \right)=ac+ad+bc+bd...........\left( 1 \right)$ .
Now, we will substitute $a=x$ , $b=7y$ , $c=7x$ and $d=-y$ . Then,
\begin{align} & \left( x+7y \right)\times \left( 7x-y \right) \\ & \Rightarrow 7{{x}^{2}}-xy+49xy-7{{y}^{2}} \\ & \Rightarrow 7{{x}^{2}}+48xy-7{{y}^{2}} \\ \end{align}
Thus, from the above result, we can say that, $\left( x+7y \right)\times \left( 7x-y \right)=7{{x}^{2}}+48xy-7{{y}^{2}}$ . Now, we can select the correct option from the given options. Then, we can say that (a) is the correct option.