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Cogito

Algebra 1 · Chapter 1 · Lesson 3

Practice Worksheet

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

NameDate

Figure — use these to answer the problems

Cut the rectangle and watch one product become the sum of two.

7 + 7 + 7 = 21

3 × 7 = 21

3 × 7 = (3 × 4) + (3 × 3) = 12 + 9 = 21

The multiplier3
Inside the bracket7
Cut after column4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Simplify 3(x + 2) + 4x. How many x?

    Answer

  2. Expand 4(x + 2). Number term?

    Answer

  3. Simplify 3x + 5x. How many x?

    Answer

  4. Expand 6(x − 3). Number term?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Simplify 2(x + 1) + 3x. How many x?

    Answer

  2. Select every pair that can be combined into one term.

    • 4x and 9x
    • 4x and 9x²
    • 6 and 11
    • 6 and 11x
    • Tick every box that applies.

  3. Simplify 2(x + 1) + 3x. What is the number term?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Is 3(x + 4) the same as 3x + 4? 1 for yes, 0 for no.

    Answer

  2. Order the steps for simplifying 5(x + 2) + 3x.

    Write 1 to 3 in the boxes to put these in order.

    • Expand the bracket
    • Collect the x terms
    • Collect the plain numbers

  3. The Bracket

    Expand 5(x + 3). What is the number term?

    Answer

  4. Collecting

    Simplify 7x + 2x. How many x?

    Answer