Distributing Letters

The distributive property works with letters the same way. $3\left(x+2\right)$ 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: $3\left(5+2\right)$ is 21, and $3\cdot 5+6$ 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.