Math Problem Solver

oduction

The famous scientist and astronomer Galileo Galilei once described mathematics as a language. The written language often uses algebra as a means of shared communication between mathematicians. Like any language, there are rules that allow the language to make sense and avoid confusion among mathematicians.

In this investigation, we investigate the rules of operations (specifically addition, subtraction, and multiplication) on terms in an expression. To do this, we use the Wolfram Alpha Calculator, here:

Wolfram Alpha Calculator https://www.wolframalpha.com/

The calculator is primarily to be used to check if your predictions and use of rules are correct. The goal is for you to analyze the patterns to figure out some of the rules of algebra on your own.

Tasks

Part A: Adding and subtracting terms

To start this investigation, we explore what happens when we add and subtract terms

(1) Use the Wolfram Alpha Calculator (see link above) to first check if the given expressions equal the simplified expressions as shown in Table 1.

Then, create at least three more expressions and state predictions for what simplified expressions would equal. Use the given examples to help you make the predictions. After you are done, use the Wolfram Alpha Calculator to check if you were correct.

[B: 1-2]

Expression Simplified expression

2𝑏+3𝑏 5𝑏

3𝑎𝑏+3𝑏 3𝑎𝑏+3𝑏

5𝑚+2𝑛+3𝑚 8𝑚+2𝑛

4𝑏+2𝑐−𝑏+4𝑐+5𝑏𝑐−3 3𝑏+6𝑐+5𝑏𝑐−3

9𝑏+3𝑏𝑎−5𝑎𝑏+4𝑎2𝑏 9𝑏+3𝑏𝑎−5𝑎𝑏+4𝑎2𝑏

Table 1

(2) Based on the results from Table 1, suggest three correct rules for adding and subtracting terms to make the simplified expressions.

Hint: Think about rules regarding the letters in terms, the order of the letters, and exponents.