Combining Like Terms and the Distributive Property

Think of terms as different units. 2x means two x's, and 5x squared means five groups of x times x — those are not the same object, so you cannot combine them any more than you'd add 2 apples and 5 boxes of apples. 2x and 5x, though, are both just x's, so they merge into 7x. The rule: terms combine only when the variable and its exponent match exactly. Numbers without a variable are their own category too, so a constant never merges with an x-term.

Distributing applies a factor outside parentheses to everything inside, one term at a time. The sign of that outside factor travels with it. So -3(x - 4) means -3 times x, which is -3x, plus -3 times -4, which is +12. The negative flips the sign of every term inside because multiplying by a negative always flips a sign. Once you've distributed, you simplify by combining whatever like terms result.

These two moves — distributing, then combining like terms — are the cleanup step behind almost every algebra question on the test. Before you can solve a linear equation, factor a quadratic, or simplify a rational expression, you first expand and collect terms into the simplest form. Get sloppy here and a correct method still produces a wrong answer, so treat this as the mechanical foundation the harder topics sit on top of.