Taking out what every term shares

A hall has 6x + 9 chairs, where x stands for a number. You want equal rows. What can go outside a bracket?

The number 3 can go outside, because 3 divides both terms. That gives 3 equal rows of 2x + 3.

Factor — a number or term that divides another exactly.

Rule: find the largest thing every term shares, number and letters. Divide each term by it. Write it outside a bracket.

At x = 4, 6x + 9 is 6 × 4 + 9 = 33. The bracket is 2 × 4 + 3 = 11, and 3 × 11 = 33.

A letter can be a factor too: 5a² + 10a = 5a(a + 2).

A number trick takes a factor out too. A digit is one of 0 to 9. Reverse the digits of 62 to get 26. Then 62 − 26 = 36 = 9 × 4.

Let t and u be the tens digit and units digit. In 62, t = 6 and u = 2, so t − u = 4. Take the bigger number first, so t is at least u. The number is 10t + u. Reversed, it is 10u + t. Subtract: (10t + u) − (10u + t) = 10t + u − 10u − t = 9t − 9u = 9(t − u).

Pick two digits. Reverse them and subtract.

Try the lab to finish this lesson.