Question

How do you simplify \[-5(8-12)\]?

Answer 1

Hint: The given expression is of the form \[a(b-c)\]. The expression \[a(b-c)\] can be written in simplified form by expanding the expression \[a(b-c)\] as \[ab-ac\], and then find the difference between these two terms.

Complete step by step answer:
We are asked to write \[-5(8-12)\] in its simplified form. This is in a similar form as of the expression \[a(b-c)\]. Here, \[a=-5\], \[b=8\], and \[c=12\]. This expression can be simplified by expanding the expression \[a(b-c)\] as \[ab-ac\], and then find the difference between these two terms.
\[a(b-c)\] can be simplified as \[ab-ac\] by expanding the bracket. So, the expression \[-5(8-12)\] can also be simplified similarly, as follows:
\[-5(8-12)\]
Expanding the bracket, we get
\[\begin{align}
  & \Rightarrow -5(8-12) \\
 & \Rightarrow -5\times 8-\left( -5 \right)\times 12 \\
\end{align}\]
Multiplying \[-5\] by \[8\] will give \[-40\], and \[-5\] by \[12\] will give \[-60\], hence the above expression can be written as,
\[\begin{align}
  & \Rightarrow -40-\left( -60 \right) \\
 & \Rightarrow 60-40=20 \\
\end{align}\]
Hence, \[-5(8-12)\] can be written in simplified form as \[20\].

Note: We can also use a second method to simplify the given expression \[-5(8-12)\]. In this method, we first have to calculate the difference between the terms present inside the bracket, and then multiply it by the term outside the bracket. This is no different from the actual meaning of the expression. Here the terms present inside the bracket are 8 and 12, we have to find the value of \[8-12\],
\[\Rightarrow 8-12=-4\]
The term outside the bracket is \[-5\], multiplying the difference between terms present inside the brackets with this value, we get
\[\Rightarrow \left( -4 \right)\times \left( -5 \right)=20\]
We can see that from both methods we are getting the same answer.