Question

Simplify the following expression: $( - 26) \times 72 + ( - 26) \times 28$

Answer 1

Hint: This question is based on the distributive property of integers that states that when an integer is multiplied with a sum of integers within parenthesis, each integer inside parenthesis is multiplied with integer outside it and then all multiples are added together to give the final product. The reverse of the property is also possible when the same integer is multiplied with different integers and added together

Formula used: For this question the reverse of distributive property is used
$a \times b + a \times c = a \times (b + c)$

Complete step-by-step solution:
Since we are required to use the reverse of the distributive property, we recognise the common integer.
$( - 26) \times 72 + ( - 26) \times 28$
The common integer in this expression is $ - 26$
So we take $ - 26$ common and add the rest of the integers so as to get a multiplicand that is easier to multiply with.
$ \Rightarrow ( - 26) \times (72 + 28)$
$ \Rightarrow ( - 26) \times (100)$
$ \Rightarrow - 2600$

As a result, we find that the value of the expression is $ - 2600$.

Additional Information: This property can be proved by multiplying the numbers individually and then adding them. One by one when you multiply integers, it is a long process and has a scope for mistakes. Using this property provides a faster and more fool proof way to make sure that not only you get the right answer you also work less than you would’ve had you multiplied separately.

Note: In cases like these, by combining the integers, we usually get an integer that is generally easier to multiply with as compared to the separate multiplications. This makes multiplication easier. Doing a single addition and simple multiplication as compared to multiple multiplications and additions is a more viable option for questions like this.