Distributing Letters

The distributive property works with letters the same way. 3(x + 2) is three copies of x + 2: x + 2 + x + 2 + x + 2. Count them up and you have three x's and three 2s, which is 3x + 6. The 3 outside multiplies every term inside: 3 times x is 3x, and 3 times 2 is 6.

Removing the parentheses this way is called expanding. The classic slip is to multiply only the first term and write 3x + 2. Test it with x = 5: 3(5 + 2) is 21, and 3 × 5 + 6 is 21 too, but 3 · 5 + 2 is only 17.

On the board, type the expanded expression as your next line. The board accepts it only if it equals the line above for every value of x, so a forgotten term is refused straight away.