Question

How do you simplify \[ - 12q(12 - q)\] ?

Answer 1

Hint: To solve the given expression, first we should know that the given expression belongs to the distributive property. Then we will discuss the steps for solving the distributive property and then simplify the expression on the basis of the following steps.

Complete step-by-step solution:
First, we will explain the steps for solving distributive property:-
Step-1: In 1st step, write the given expression in the form of \[a(b + c)\] i.e.. the general structure of Distributive property.
Step-2: Now, apply the distributive property completely, i.e.. \[a(b + c) = ab + ac\]
Step-3: After putting the given respective values, we will get the final simplified expression i.e.. \[ab + ac\] with their greater signs.
Step-4: And, finally rearrange the terms in the descending order of the power.
Now, we will go to solve for the given expression:
Given expression-
\[ - 12q(12 - q)\]
Apply the distributive property:
$a(b + c) = ab + ac$ , where $a = - 12q$ , $b = 12$ and $c = - q$
Now, put the value of a,b and c respectively in the above expression:
$
  \Rightarrow ( - 12q)(12) + ( - 12q)( - q) \\
   \Rightarrow - 144q + 12{q^2} \\
$
Rearrange the terms in the descending order of the power:
$\because 12{q^2} - 144q$

Hence, the simplified form of the expression \[ - 12q(12 - q)\] is $12{q^2} - 144q$ .

Note: This property states that two or more terms in addition or subtraction with a number are equal to the addition or subtraction of the product of each of the terms with that number. This property is almost used in every sector or topics of mathematics.