Question

Compare which is greater:

$\left(6-8\right)\times \left(-10\right)\mathrm{or}6\times \left(-8\right)\times \left(-10\right)$

Answer 1

$$\begin{gathered} \left(6-8\right)\times \left(-10\right) \\ =\left(-2\right)\times \left(-10\right)\left[\left(-\right)\times \left(-\right)=\left(+\right)\right] \\ =20 \end{gathered}$$

$$\begin{gathered} \left(6\right)\times \left(-8\right)\times \left(-10\right)\left[\left(+\right)\times \left(-\right)=\left(-\right)\right] \\ =-\left(6\times 8\right)\times \left(-10\right) \\ =\left(-48\right)\times \left(-10\right)\left[\left(-\right)\times \left(-\right)=\left(+\right)\right] \\ =480 \end{gathered}$$

$$\begin{gathered} 20<480 \\ \Rightarrow \left(6-8\right)\times \left(-10\right)<6\times \left(-8\right)\times \left(-10\right) \end{gathered}$$

Hence, $6\times \left(-8\right)\times \left(-10\right)$ is greater.