How do you simplify $-3\cdot 12-18+72+8\cdot 75$?

Hint: In the above question, we have been given a mathematical equation to simplify, which is \[-3\cdot 12-18+72+8\cdot 75\]. In this mathematical expression, there are many mathematical operators present. These are the subtraction, the addition, and the multiplication. To simplify it, we need an order of these three mathematical operators, which is given by the BODMAS rule. BODMAS stands for “Bracket Open Division Multiplication, Addition, and Subtraction”. From this rule, we have to perform multiplication first, then addition and subtraction. Therefore, we will perform the multiplication of the first two terms \[-3\cdot 12\], then subtraction, then addition and so on to get the final simplified result.

Complete step-by-step answer:
Let us write the mathematical expression given in the above question as
$\Rightarrow E=-3\cdot 12-18+72+8\cdot 75$
Since there are many mathematical operators involved in the above expression, therefore, in order to simplify it, we need to follow a specific order of these mathematical operations. From the above expression, we can see that these operations are the subtraction, the addition, and the multiplication. For this, we use the BODMAS rule. We know that BODMAS stands for “Bracket Open Division Multiplication, Addition, and Subtraction”. Therefore, we first solve for the first multiplication encountered. The first product is $-3\cdot 12$ which equates to \[-36\]. Therefore, the above expression gets reduced to
$\Rightarrow E=-36-18+72+8\cdot 75$
Now, we can perform the subtraction of the first two terms to get
$\Rightarrow E=-54+72+8\cdot 75$
Now, adding the first two terms, we get
$\Rightarrow E=18+8\cdot 75$
Now, we have addition and multiplication. But according to the BODMAS rule, we perform the multiplication $8\cdot 75$ first, to write the above expression as
$\Rightarrow E=18+600$
Finally, on adding the two terms, we get
$\Rightarrow E=618$
Hence, the given expression has been simplified to $618$.

Note: Since multiplication is to be preferred first, we can solve all the precuts present in the given expression and then perform the necessary addition and subtraction. By doing this also, we will get the same result. Also, we can also use the PEMDAS rule, which also gives the order of the use of mathematical operators.