Chapter 7.4, Problem 17HP

To determine

Explain how you can use a rule for subtracting integers to help subtract linear expression

Explanation of Solution

Concept Used:

To subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same. on the variables the same.

Rule for subtracting the integers:

Rule 1: When the two numbers are with same sign (positive or negative) always add the numbers and put their corresponding sign of the numbers (positive or negative)

Example: 78 + 90 = 168 (both are positive)

− 78 − 90 = − 168 (both numbers are negative)

Rule 2: When one number is positive and other number is negative, always do the subtraction and put the sign of the bigger number.

Example: − 78 + 178 = + 100 (as the bigger number 178 is positive, so the answer will be positive after the subtraction).

Example: +78 − 178 = − 100 (as the bigger number 178 is Negative, so the answer will be Negative after the subtraction).

Rule for subtracting the linear expression: $(a+b)-(c-d)=a+d-c+d$ (change the sign of the 2^nd expression $(c-d)$ which is subtracted from the 1^st expression $(a+b)$ ).

Example:

  $\begin{array}{l}(12a+7b)-(6a-9b)\\ 12a+7b-6a+9b[\text{change}\text{the}\text{signs}\text{of}\text{the}\text{exp}(6a-9b)]\\ 12a-6a+7b+9b[\text{add}\text{the}\text{like}\text{terms}]\\ 6a+16b\\ (12a+7b)-(6a-9b)=6a+16b\end{array}$