Cogito
Algebra 1 · Chapter 1 · Lesson 3
Distributing and Collecting
Two moves that do most of the work in algebra.
11 problems · about 22 minutes · A-SSE.A.1, A-APR.A.1
What this lesson teaches
The student expands a product over a sum and collects like terms to simplify an expression.
- A multiplier outside a bracket reaches every term inside it.
- Terms combine only when their letter parts match exactly.
- Expanding and collecting first makes the equation that follows much shorter.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSimplify 3(x + 2) + 4x. How many x?
Answer 7
Why 7x + 6.
Expand 4(x + 2). Number term?
Answer 8
Why 4 × 2.
Simplify 3x + 5x. How many x?
Answer 8
Why Add the counts.
Expand 6(x − 3). Number term?
Answer -18
Why The sign travels too.
Build It Up
The same ideas with more to keep track of.
3 problemsSimplify 2(x + 1) + 3x. How many x?
Answer 5
Why 2x and 3x.
Select every pair that can be combined into one term.
Answer 4x and 9x; 6 and 11
Why The letter part must match exactly.
Simplify 2(x + 1) + 3x. What is the number term?
Answer 2
Why Only the 2 from the bracket.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsIs 3(x + 4) the same as 3x + 4? 1 for yes, 0 for no.
Answer 0
Why Try x = 1.
Order the steps for simplifying 5(x + 2) + 3x.
Answer 1. Expand the bracket 2. Collect the x terms 3. Collect the plain numbers
Why Nothing can be collected while it is still inside a bracket.
The Bracket: Expand 5(x + 3). What is the number term?
Answer 15
Why 5x + 15.
Collecting: Simplify 7x + 2x. How many x?
Answer 9
Why 9x.