Question

How do you combine like terms in `(5x^2+4)-(3x+7)+(2x^2-1)`?

Answer 1

`7x^2 - 3x - 4`

Explanation:

Like terms are defined as terms with the same variables that are raised to the same power.

For example, the terms `ax` and `bx^2` are NOT like terms because the coefficients `a` and `b` have variables (`x` and `x^2`, respectively) that are not raised to the same power.

In the expression `(5x^2+4)-(3x+7)+(2x^2-1)`, the like terms are grouped as follows:
`5x^2` and `2x^2`

`-3x` (this is negative because the subtraction sign is "distributed" to the terms inside of the parentheses)

`4`, `-7`, `-1` (the reason for why it's `-7` is the same reason for why `-3x` is negative)

Add the terms in the groups up...
`5x^2 + 2x^2 = 7x^2`
`-3x`
`4 - 7 - 1 = -4`

Now you have the simplified expression: `7x^2 - 3x - 4`