a(b + c) ≠ ab + c: the distribution slip on SAT Algebra
3(x + 4) = 3x + 4 looks fine at 2am with 20 seconds per question. It isn't.
Why it happens
Your eye latches onto the first term, distributes once, and moves on. The parenthesis silently loses its second multiplication.
See the trap
Simplify 5(x + 2) = 40.
✗ The trap: 5x + 2 = 40 → 5x = 38 → x = 7.6.
✓ The fix: 5x + 10 = 40 → 5x = 30 → x = 6.
How to actually fix it
- Draw arrows from the outside factor to EVERY term inside.
- Count: n terms inside means n multiplications written out.
- When stuck between two answers, re-expand the original expression.
Made this mistake on a real question?
Practice Algebra questions here. Miss one and it is logged with the exact error, then brought back until you beat it.
Practice Algebra →FAQ
Does this show up with negative signs too?
Constantly — −(x − 3) = −x + 3 is the same trap wearing a minus sign. Treat the minus as multiplying by −1 and distribute it to every term.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.