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.
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 − 6 — both 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.