Prove that 2(a-b) 2(a+b)=8(a b) - Vidyadip

Question

Prove that $2(\bar{a}-\bar{b}) \times 2(\bar{a}+\bar{b})=8(\bar{a} \times \bar{b})$

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Answer

$\begin{aligned} \text { LHS } & =2(\bar{a}-\bar{b}) \times 2(\bar{a}+\bar{b}) \\ & =4[(\bar{a}-\bar{b}) \times(\bar{a}+\bar{b})] \\ & =4[\bar{a} \times(\bar{a}+\bar{b})-\bar{b} \times(\bar{a}+\bar{b})] \\ & =4(\bar{a} \times \bar{a}+\bar{a} \times \bar{b}-\bar{b} \times \bar{a}-\bar{b} \times \bar{b}) \\ & =8(\bar{a} \times \bar{b})\end{aligned}$

$\ldots[\because \bar{a} \times \bar{a}=\bar{b} \times \bar{b}=\overline{0}$ and $-(\bar{b} \times \bar{a})=\bar{a} \times \bar{b}]$

$=\mathrm{RHS}$

$\therefore 2(\bar{a}-\bar{b}) \times 2(\bar{a}+\bar{b})=8(\bar{a} \times \bar{b})$.

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