Expand, Then Combine · Deep Dive 5

Two moves, one line at a time

Longer problems use both big moves. First, expand every set of parentheses. Then combine like terms. Do it in that order, and write each step on its own line.

2(x + 3) + 4(x − 1)2x + 6 + 4(x + ⁻1) expand the first group2x + 6 + 4x + ⁻4 expand the second group(2x + 4x) + (6 + ⁻4) move like terms together6x + 2

5 − 2(3x − 4)5 + ⁻2(3x + ⁻4) adding the opposite5 + ⁻6x + 8 hand out ⁻2⁻6x + 13

Wrong

5 − 2(3x − 4)3(3x − 4)

5 − 2 was done first.

Right

5 − 2(3x − 4)5 + ⁻2(3x + ⁻4)5 + ⁻6x + 8⁻6x + 13

Multiply before you add.

The 2 belongs to the parentheses, so multiply before you add: the order of operations from Unit 3, Lesson 7. The minus sign goes with the 2, so hand out ⁻2.

Elle and Finn

ElleMath-speak

To simplify, apply the distributive property first, then combine like terms.

FinnPlain English

Open the parentheses first, then sort and count. Never add the number in front to something outside.

A real one

Four friends each buy a movie ticket for t dollars and a 3 dollar snack. They use one 5 dollar coupon.

4(t + 3) − 5 total cost4t + 12 + ⁻5 expand, adding the opposite4t + 7 dollars

Let me try a few

NC standard: NC.7.EE.1.

Where to go next

Let me try a few7 problems on expand, then combine. All tilesAll 3 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.