can terms be added and subtracted?

Answer 1

Like terms can be added or subtracted.

5 Apples + 6 Apples = 11 Apples

Let A = An Apple: 5A + 6A = 11A

However, if the terms are not like, you cannot add or subtract them.

5 Apples - 3 Bananas = ????

Let A = An Apple, B = A Banana: 5A - 3B = ???

Like terms should share the same units, power, coefficients etc.

Like Units:

5 in + 3 in = 8 inches

5 in + 1 foot = 5 in + 12 in = 17 in <--- here we had to convert a unit

Unlike Units:

5 inches + 9 seconds = ???

3 rubber bands + 1 light year = ???

Like Powers:

5A2 + 9A2 = 14A2

6 square feet + 4 square feet = 10 square feet

Unlike Powers:

5A2 + 5A3 = (5A2)(1+A) = ???? <--- i was able to simplify a little here, but still not combine all terms

6 meter/second + 1 meter/second2 = ???

Like Coefficients:

10A + 90A = 100A

2AB + 3BA = 2AB + 3AB = 5AB <--- this is just a multiplicative property (AB=BA)

Unlike Coefficients:

10A + 9B + 8C = ???