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The Distributive Law (expanding)
Rung 3 of 4 · The traps

The Two Slips Everyone Makes

Expanding goes wrong in exactly two places: forgetting the second term, and losing a minus sign. Spot them once and you'll never lose those marks again.


Spot itTap the line that's wrong, then read why. Flip on “− sign out the front” for the nastier ones.
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The maths itself is easy. The marks get lost in two tiny, predictable spots — and both are about being thorough, not clever.

Slip One — Only Doing the First Term

This is the big one. People write 3(x + 4) = 3x + 4, multiplying the x but leaving the 4 sitting there untouched. The outside number has to reach every term inside the brackets — that's the whole point of "distributing". The correct line is 3x + 12. In the toy, this is the slip where one term looks suspiciously unchanged.

Say it plainly: the number outside multiplies every single term inside the brackets — not just the first one. Two terms inside means two multiplications, always.

Slip Two — Losing the Minus Sign

Signs are sneaky. In 3(2x − 5) the second term is negative five, so 3 × (−5) = −15, giving 6x − 15. People rush and write 6x + 15, dropping the minus. The sign travels with the term it's attached to — never leave it behind.

The Big One — a Minus Out the Front

Here's the trap worth real marks. −2(x + 3) means negative two multiplies both terms. −2 × x = −2x and −2 × 3 = −6, so the answer is −2x − 6both signs flipped, even though the second one was a plus inside. And −2(x − 3)? That's −2x + 6, because negative times negative is positive. Flip on "− sign out the front" in the toy and drill this until flipping both signs is a reflex.

Us, Thinking Out Loud

What's a quick way to remind yourself to multiply the second term too?

Why does a minus out the front flip both signs, even the plus one?