Multiplying a bracket by one term

A trick says: "Take your age. Times 3. Add 5. Times 2." What is that as one line?

The one line is 2(3a + 5), which opens to 6a + 10. Opening a bracket means multiplying each term inside by the term outside.

Rule: a term outside a bracket multiplies every term inside it. Each product follows term times term.

Because 2(3a + 5) is 3a + 5 added to itself, every term is doubled.

At age 12, a = 12. The bracket is 3 × 12 + 5 = 41. Then 2 × 41 = 82. Opened, 6a + 10 is 6 × 12 + 10 = 72 + 10 = 82.

A minus inside works the same way. Here 3a × 2a = 6a² and 3a × 4 = 12a. So 3a(2a − 4) = 6a² − 12a.

Slide the age. Both ways give one answer.