Simplify 3x² + 2x − x² + 5x − 7 by combining like terms.

Step-by-step solution

1. 1

   Identify which terms are actually alike. Only terms with the same variable raised to the same power can be merged. Here there are three groups:

   $\underbrace{3x^2,\ -x^2}_{\text{degree }2} \qquad \underbrace{2x,\ 5x}_{\text{degree }1} \qquad \underbrace{-7}_{\text{constant}}$

   The $x^2$ terms and the $x$ terms cannot be combined with each other, which is the single most common error on this kind of problem.

2. 2

   Attach each sign to the term that follows it. Reading left to right, the coefficients are $+3$, $+2$, $-1$, $+5$, $-7$. In particular $-x^2$ means the coefficient is $-1$, not $0$ — the invisible $1$ still counts.

3. 3

   Combine the quadratic terms. Add the coefficients and keep $x^2$ unchanged:

   $3x^2 - x^2 = (3 - 1)x^2 = 2x^2$

4. 4

   Combine the linear terms.

   $2x + 5x = (2 + 5)x = 7x$

   The constant $-7$ stands alone because there is no other pure number in the expression.

5. 5

   Write the simplified expression in standard form. Ordering by descending degree:

   $2x^2 + 7x - 7$

   Check by substituting $x = 2$ into both versions: the original gives $12 + 4 - 4 + 10 - 7 = 15$, and the simplified form gives $8 + 14 - 7 = 15$.