How many terms are in this expression $5\left( -4a+8b+7c \right)-3\left( 5b-11c-32 \right)$?

Hint: From the question we have been asked to find how many terms there are in$5\left( -4a+8b+7c \right)-3\left( 5b-11c-32 \right)$. For this question we will expand the terms inside the brackets using multiplication with the terms outside the brackets. By doing the multiplication next we will add the terms of the same variable and simplify them. In this way we will solve the questions.

Complete step-by-step solution:
Firstly, we will use the basic mathematical operation which is multiplication and simplify the terms $\left( -4a+8b+7c \right)$ and $\left( 5b-11c-32 \right)$ by multiplying them with $5$ and $-3$ respectively.
So, in the first case we will expand the term $\left( -4a+8b+7c \right)$. So, the equation will be reduced as follows.
$\Rightarrow 5\left( -4a+8b+7c \right)-3\left( 5b-11c-32 \right)$
$\Rightarrow -20a+40b+35c-3\left( 5b-11c-32 \right)$
Now, we will expand the other term. So, the equation will be further reduced as follows.
$\Rightarrow -20a+40b+35c-3\left( 5b-11c-32 \right)$
$\Rightarrow -20a+40b+35c-15b+33c+96$
Here in the question, we have been asked to find how many terms. So, we will rearrange the terms which we got in the equation. So, after rearranging we get the reduced as follows.
$\Rightarrow -20a+40b+35c-15b+33c+96$
$\Rightarrow -20a+40b-15b+35c+33c+96$
Here we will use the basic operation which is addition and simplify the equation. So, we get the equation simplified as follows.
$\Rightarrow -20a+40b-15b+35c+33c+96$
$\Rightarrow -20a+25b+68c+96$
Therefore, the number of terms for the given question is $4$.

Note: Students must be very careful in doing the calculations. Students should perform the basic operations which are multiplication and addition without any mistake. Here we should add only terms or variables in these questions. We should not make mistakes like adding the unlike terms or variables to each other.