Question

Find the product, using suitable properties: $\left(-57\right)\times \left(-19\right)+57$

Answer 1

Simplify using the distributive law of multiplication:

According to the distributive law of multiplication over addition,

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

The given expression is $\left(-57\right)\times \left(-19\right)+57$.

Then, the required product is,

$\left(-57\right)\times \left(-19\right)+57=\left(57\right)\times \left(19\right)+57$ $\left[\because \left(-a\right)\left(-b\right)=a\times b\right]$

$\Rightarrow \left(-57\right)\times \left(-19\right)+57=57\times 19+57\times 1$ $\left[\because 1\times n=n\right]$

$\Rightarrow \left(-57\right)\times \left(-19\right)+57=57\times \left(19+1\right)$ $[\because a\times b+a\times c=a\times (b+c)]$

$\Rightarrow \left(-57\right)\times \left(-19\right)+57=57\times \left(20\right)$

$\Rightarrow \left(-57\right)\times \left(-19\right)+57=1140$

Hence, the product of $\left(-57\right)\times \left(-19\right)+57$ is $1140$.