Question

Find the product, using suitable properties: $\left(-41\right)\times 102$

Answer 1

Simplify using the distributive law of multiplication:

According to the distributive law of multiplication over addition,

$a\times \left(b+c\right)=a\times b+a\times c$

The given expression is $\left(-41\right)\times 102$.

Then, the required product is,

$\left(-41\right)\times 102=\left(-41\right)\times \left(100+2\right)$ $\left[\because a\times \left(b+c\right)=a\times b+a\times c\right]$

$\Rightarrow \left(-41\right)\times 102=\left(-41\right)\times 100+\left(-41\right)\times 2$ $[\because -\left(-a\right)=+a]$

$\Rightarrow \left(-41\right)\times 102=\left(-4100\right)+\left(-82\right)$

$\Rightarrow \left(-41\right)\times 102=-4100-82$ $\left[\because \left(-a\right)\left(-b\right)=a\times b\right]$

$\Rightarrow \left(-41\right)\times 102=-4182$

Hence, the product of $\left(-41\right)\times 102$ is $-4182$.