Leo+DadMade for Leo
The Distributive Law (expanding)
Rung 2 of 4 · The method

Actually Expanding One

One rule, used twice: hit the first term, hit the second term, write them both down. Pronumerals and negatives don't change the move at all.


PractiseHit “new expression”, expand it, then check. Use “show me the steps” if you get stuck.
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Every expanding question is the same two strokes: outside × first term, then outside × second term. Write both results out, keeping their signs, and you're done.

The Two Strokes

One — multiply the outside number by the first term inside. If it's 3(x + 4), that's 3 × x = 3x.

Two — multiply the outside number by the second term. 3 × 4 = 12. Then just write them together: 3(x + 4) = 3x + 12. Done.

A Worked One

Expand 5(2a + 3). First stroke: 5 × 2a = 10a. Second stroke: 5 × 3 = 15. Put them together: 5(2a + 3) = 10a + 15. Notice 5 × 2a means multiply the number part (5 × 2 = 10) and carry the a along.

Carry the sign: the plus or minus belongs to the term after it. In 4(x − 2) the second term is negative two, so it's 4 × (−2) = −8, giving 4x − 8. The sign rides along with the number.

Negatives Are No Different

If a term inside is being subtracted, treat it as a negative and multiply normally. 6(n − 5) = 6n − 30. A negative inside times a positive outside stays negative — same multiplication rules you already know, no special case to memorise. Run the toy until expanding feels as automatic as your times tables.

Us, Thinking Out Loud

Could you talk me through the two strokes without looking?

Why does the minus sign belong to the term after it?