How do you add like terms with exponents?

Question

This isn't the 3rd grade type of adding like terms, but the Algebra one type. 

Answer 1

First, lets talk about what like terms are. When we talk about like terms in math, we are talking about two terms that have the same number of EACH variable.
EXAMPLES:

2xy and 5xy are like terms because they each have 1 x and 1 y

x and x² are NOT like terms because the first term has 1 x and the second has 2

4xy² and 7y²x are Like terms because they each have 1 x and 2 y

4 and 5 are Like terms because they don't have any variables

Usually in an equation, there are many terms added and subtracted from each other. "combining like terms" means identifying any like terms and either adding or subtracting them (depending on what the equation says)

EX.

4+2x-x²-1+3x+2x²
1. identify like terms (I have color-coded)

4+2x-x²-1+3x+2x²

2. Rearrange to put like terms next to each other

4-1+2x+3x-x²+2x²

3. Add/subtract like terms

3+5x+x²

Comment if you need more help

Answer 2

Ember,

 

Remember 2 things.  First, while you still have unknown letters in an Algebraic expression, different powers and cross terms are different "fruits" like grapes and oranges are different so you can't add them then. You have to add all the grapes separately, all the oranges separately, etc. Second, only the numbers or coefficients can be added for each type of fruit.  Of course, once you have numerical solutions for all the unknowns, you can substitute their numbers for the unknowns, and every term becomes a number, so all can then be added together.  Thus x⁷ is different from x⁵ is different from y id different from xy is different from x⁴y², etc.

 

Formally, you simplify expressions by using the Distributive Law in reverse using the "fruits" as multipliers and having only numerical coefficients inside their parenthesis, then combining these coefficients into a single number for that fruit.  For example:

 

Algebraic Expression:  -3x⁶ + 2 xy² +14x⁶ - 6x²y - 12xy² - 4x⁴ + x⁶ -36y        becomes

                                 x⁶(-3 + 14 + 1) + xy²(+2 -12) + x²y(-6 + 0)) + x⁴(-4 + 0) + y(-36 + 0)

                                 x⁶(12)               +xy²(-10)       + x²y(-6)        + x⁴(-4)       + y(-36)

Then it is customary to place the coefficients before the letters and rearrange the terms in descending powers of x and ascending powers of y if possible.

 

So the simplified expression becomes:  12x⁶ - 4x⁴ - 6x²y - 10 xy² - 36y