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

Mar 24, 2018

$7 {x}^{2} - 3 x - 4$

#### Explanation:

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

For example, the terms $a x$ and $b {x}^{2}$ 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 $\left(5 {x}^{2} + 4\right) - \left(3 x + 7\right) + \left(2 {x}^{2} - 1\right)$, the like terms are grouped as follows:
$5 {x}^{2}$ and $2 {x}^{2}$

$- 3 x$ (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 $- 3 x$ is negative)

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

Now you have the simplified expression: $7 {x}^{2} - 3 x - 4$