Question

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

Answer 1

Hint: We will solve this question by using distributive property. So, we will suppose $a = - \,48,b = 26andc = - 36$.Thereafter we will put these values in distributive property.by using distributive property: $ab + ac = a\left( {b + c} \right)$.


Complete step by step solution:
Here,
$
  a = - \,48 \\
  b = 26 \\
  c = - 36 \\
 $
$26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = a\left( {b + c} \right)$ …(i)
Put the value of a, b and c in equation (i),we will get.
 $26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = - 48\left( {26 + \left( { - 36} \right)} \right)$
$26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = - 48\left( {26 - 36} \right)$
$26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = - 48 - \left( {10} \right)$ [two negative number in multiply their answer will be in positive number]
$26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = 48$


Note: Students must know that when two negative numbers multiply their answer will be in positive number, if one positive number and one negative number in multiply their answer will be negative number.