Generate equivalent expressions · lesson

The distributive property

💡 To multiply out parentheses, multiply the outside number by every term inside.

The distributive property says a(b + c) = ab + ac. The outside number multiplies each term inside.

If there is a minus sign inside, keep it. 3(5 − x) is 15 − 3x.

🧠 Let's work it out

Multiply out 4(x + 6).

What do you think comes next?

distributive property: a(b + c) = ab + ac: the outside number multiplies each term inside
term: a part of an expression added or subtracted, like 4x or 24

💡 Add or subtract terms with the same letter, and add the plain numbers separately.

Like terms have the same letter part. 5x and 3x are like terms. 5x and 3 are not.

To combine, add the numbers in front, called coefficients. A letter alone, like y, has a coefficient of 1.

Plain numbers are like terms with each other.

🧠 Let's work it out

Simplify 5x + 2 + 3x + 4.

What do you think comes next?

💡 Factoring undoes the distributive property: pull the greatest common factor outside the parentheses.

Factoring goes the other way. You start with a sum and write it as a product.

Find the greatest common factor (GCF) of the numbers. Put it outside. Divide each term by it to see what goes inside.

🧠 Let's work it out

Factor 14x + 21.

What do you think comes next?

💡 Clear every set of parentheses first, then combine the like terms.

Some expressions have two sets of parentheses. Multiply out each one first.

Then group the x terms and the plain numbers, and combine each group.

🧠 Let's work it out

Simplify 3(x + 2) + 2(x + 5).

What do you think comes next?