Section 1.2
Substitution
It is important when substituting numerical values for variables that the indicated arithmetic follow the substitution. Don't try to do both the substitution and the arithmetic simultaneously. This is particularly important when the arithmetic is subtraction. One particular area for confusion comes when there is a minus sign that represents an opposite, rather than subtraction, in front of a variable; and the confusion seems to be compounded when the variable represents a negative number. Remember that if there are no parentheses, then use exponents first; hence in the expression $-x^2$, the variable $x$ must be squared before the minus sign is applied.
Example:
If $x=-2$ and $y=3$, then evaluate $2xy-x^2$.
\begin{align}
2xy-x^2&=2\cdot(-2)\cdot 3-(-2)^2\\
&=-12-4\\
&=-16
\end{align}
Exercises:
In the following problems, let $a=-2,\text{ }b=3,\text{ and }c=-4$. Evaluate each expression.
\begin{array}{l l l}
1. \;\;{{a}^{2}}b-c\;\; & 2. \;\;a-{{a}^{2}}\;\; &3. \;\;abc+{{b}^{3}}\;\;\\
4. \;\;-{{a}^{2}}-{{c}^{2}}\;\; & 5. \;\;a+b-c\;\; &6. \;\;2a-3b+4c\;\;\\
7. \;\;-a+bc\;\; & 8. \;\;-a-ac\;\; & 9. \;\;a+abc\;\;\\
10. \;\;bc-ac\;\; & 11. \;\;2b+3ac\;\; & 12. \;\;3a-2{{b}^{2}}c\;\;\\
13. \;\;1-2a+3b-4c\;\; & 14. \;\;2{{a}^{2}}-{{b}^{2}}\;\; & 15. \;\;{{c}^{3}}-{{b}^{2}}-a\;\;\\
16. \;\;-{{c}^{3}}+ab\;\; & 17. \;\;(a+b)(a+c)\;\; & 18. \;\;\left( {{a}^{2}}-c \right){{\left( a-b \right)}^{2}}\;\;\\
19. \;\;2+3(a-b+c)\;\; & 20. \;\;{{a}^{b}}\cdot {{b}^{-a}}\;\; & 21. \;\;-{{a}^{b}}\;\;\\
22. \;\;{{\left( a+b+c \right)}^{b}}\;\; & 23. \;\;a\div c-bc\;\; & 24. \;\;{{(4-b)}^{ac}}\;\;\\
25. \;\;1\div a\cdot b\div c\;\; & 26. \;\;3\left( {{a}^{b}}-2c \right)\;\; & 27. \;\;2\cdot a-b\cdot c\;\;\\
28. \;\;{{5}^{a+b}}\cdot c\;\; & 29. \;\;{{2}^{ac-2b}}\div (4a)\;\; & 30. \;\;a\cdot b\cdot c\div a\cdot b\cdot c\;\;\\
\end{array}