Question

Find the product, using suitable properties: $\left(-17\right)\times \left(-29\right)$

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 $\left(-17\right)\times \left(-29\right)$.

Then, the required product is,

$\left(-17\right)\times \left(-29\right)=17\times 29$ $\left[\because \left(-a\right)\times \left(-b\right)=a\times b\right]$

$\Rightarrow \left(-17\right)\times \left(-29\right)=17\times \left(30-1\right)$ $\left[\because 29=30-1\right]$

$\Rightarrow \left(-17\right)\times \left(-29\right)=17\times 30-17\times 1$

$\Rightarrow \left(-17\right)\times \left(-29\right)=510-17$

$\Rightarrow \left(-17\right)\times \left(-29\right)=493$

Hence, the product of $\left(-17\right)\times \left(-29\right)$ is $493$.