Simplifying Expressions

Like terms have the exact same variable part. $3x$ and $2x$ are like terms; $5$ and $7$ are like terms; but $3x$ and $5$ are not — you can't combine them. Combining like terms just means adding their coefficients: $3x + 2x = 5x$, while the lone numbers add separately.

The distributive property handles parentheses: $a(b + c) = ab + ac$. The outside factor multiplies every term inside — both of them, not just the first. That's the most common slip, so watch it: $3(x + 4) = 3x + 12$, not $3x + 4$.

Combine like terms — match them up, add separately:

$3x + 5 + 2x = (3x + 2x) + 5 = 5x + 5$

The $5$ has no like term, so it just rides along.

Distribute — multiply the outside number into each term:

$3(2x + 4) = 3 \cdot 2x + 3 \cdot 4 = 6x + 12$

Both together — distribute first, then combine:

$2(x + 3) + 4x = 2x + 6 + 4x = 6x + 6$

The result $6x + 6$ is fully simplified: one $x$-term, one number, nothing left to combine.

Distribute the factor to every term inside the parentheses. Predict before you check.