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

Hint: In this question we have to find the final product of all the terms given to us in the expression. We will start solving the question by using the mathematical property of taking out the common term from both the expressions and write it in multiplication form. We will then expand brackets and solve the signs of the terms and simplify the expression to get the required solution.

Complete step by step solution:
We have the expression given to us as:
$\Rightarrow 26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right)$
We can see that the term $\left( -48 \right)$ is common in both the terms which are in addition therefore on taking them out as common, we get:
\[\Rightarrow \left( -48 \right)\times \left[ 26+\left( -36 \right) \right]\]
On simplifying the bracket, we get:
\[\Rightarrow \left( -48 \right)\times \left[ 26-36 \right]\]
Now in the square bracket, we have the greater term which has a negative sign and the smaller term has a positive sign therefore, the result of their subtraction will be negative. On subtracting, we get:
\[\Rightarrow \left( -48 \right)\times \left[ -10 \right]\]
Now on opening the brackets, we get:
\[\Rightarrow -48\times -10\]
Now since there are two negative terms in multiplication, the multiplication of both the terms will be positive therefore, on multiplying, we get:

$\Rightarrow 480$, which is the required solution.

Note: It is to be remembered that whenever there are various arithmetic operations in succession like addition, subtraction, multiplication and division the rule of $\text{BODMAS}$, which is the acronym for brackets orders of division, multiplication, addition and subtraction. The operations written first are supposed to be done first similarly how we first did the multiplication operation first and then addition.