5 Common Algebra Mistakes (And How to Stop Making Them)

After years of tutoring, the same five algebra mistakes come up over and over. They’re not random — each has a specific cause and a specific fix.

Quick answer

The big five: sign errors when distributing negatives, dropping the ± when taking square roots, forgetting to check both solutions of a quadratic, mishandling fractions inside equations, and treating x² + y² as (x + y)². Fix each by slowing down at one specific step.

Mistake 1: Sign errors when distributing

−(3x − 5) becomes −3x + 5, not −3x − 5. The negative distributes to EVERY term inside the parentheses.

Fix: when you see a negative outside parentheses, draw a quick arrow to each term inside and flip the sign one at a time.

Mistake 2: Dropping the ± with square roots

If x² = 16, then x = +4 OR x = −4. Most students only write x = 4 and lose the other answer.

Fix: any time you take a square root of both sides, write ± immediately. Then check whether both solutions make sense in context.

Mistake 3: Forgetting one solution of a quadratic

A quadratic equation almost always has two solutions. After factoring (x − 3)(x + 5) = 0, write BOTH x = 3 and x = −5.

Fix: after factoring, draw a horizontal line under each factor and solve each one separately.

Mistake 4: Fractions inside an equation

(x / 2) + (x / 3) = 5. Most students try to combine fractions first. Easier: multiply both sides by 6 to clear all fractions at once. 3x + 2x = 30 → x = 6.

Fix: when you see fractions in an equation, multiply both sides by the LCD before doing anything else.

Mistake 5: (x + y)² = x² + y² (wrong!)

The correct expansion is (x + y)² = x² + 2xy + y². The cross term 2xy is what people forget.

Fix: always expand FOIL the first few times instead of using shortcuts. Once the pattern is automatic, you can shortcut safely.

How to drill these

Pick the mistake you make most often. Work 10 problems where that specific step shows up. Mark each one and write what you did vs. what you should have done. Two days of focused drill kills the habit.