Question

Find the product, using suitable properties: $26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)$

Answer 1

Simplify using the distributive law of multiplication:

According to the distributive law of multiplication over addition,

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

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

The given expression is $26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)$.

Then, the required product is,

$26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)=\left(-48\right)\left[26+\left(-36\right)\right]$ $\left[\because a\times b+a\times c=a\times \left(b+c\right)\right]$

$\Rightarrow 26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)=\left(-48\right)\left[26-36\right]$ $[\because -\left(-a\right)=+a]$

$\Rightarrow 26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)=\left(-48\right)\left(-10\right)$

$\Rightarrow 26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)=\left(48\right)\left(10\right)$ $\left[\because \left(-a\right)\left(-b\right)=a\times b\right]$

$\Rightarrow 26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)=480$

Hence, the product of $26\times \left(-48\right)+\left(-48\right)\times \left(-36\right)$ is $480$.