Simplifying · Two Variables · C5

Distribute then collect.

Expand the bracket, then collect each letter: 2(x + y) + 4x = 2x + 2y + 4x = 6x + 2y.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute then collect (2)

2(x + y) + 4x: expand to 2x + 2y + 4x, collect → 6x + 2y.

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2(x+y)+4x2(x + y) + 4x
1

Distribute

Multiply out the brackets — every term inside by the factor in front.

2x+2y+4x2x + 2y + 4x
2

Group like terms

Gather the terms that share the same variable part.

(2x+4x)+2y(2x + 4x) + 2y
3

Combine

Add the coefficients within each group.

6x+2y6x + 2y
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

Type the simplest form (e.g. 6x + 5). Use ^ for powers.

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— / WHY IT WORKS

The idea underneath.

Two steps, two letters

Expand first, then gather xs and ys. The y-term often has nothing to combine with — it just carries through.

Why it works

Open the box, then sort into x and y piles.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

3(x + y) + 2x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 3x + 3y + 2x

2

Group like terms

Gather the terms that share the same variable part. → (3x + 2x) + 3y

3

Combine

Add the coefficients within each group. → 5x + 3y

EX 2medium

9(x + y) + 5x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 9x + 9y + 5x

2

Group like terms

Gather the terms that share the same variable part. → (9x + 5x) + 9y

3

Combine

Add the coefficients within each group. → 14x + 9y

EX 3hard

6(x + y) + 5x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 6x + 6y + 5x

2

Group like terms

Gather the terms that share the same variable part. → (6x + 5x) + 6y

3

Combine

Add the coefficients within each group. → 11x + 6y

04 / COMMON TRAPS

Where students slip.

Trap

Combining the y into the xs.

Fix

Different letters stay apart.

Trap

Skipping the expand step.

Fix

Distribute before collecting.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Simplify 3(x + y) + 2x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
C2

Simplify 3(x + y) + 3x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
C3

Simplify 5(x + y) + 3x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
C4

Simplify 6(x + y) + 5x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
Apply

Apply (4)

A1

Simplify 9(x + y) + 5x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
A2

Simplify 4(x + y) + 3x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
A3

Simplify 8(x + y) + 5x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
A4

Simplify 7(x + y) + 3x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
Extension

Extension (4)

E1

Simplify 6(x + y) + 5x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
E2

Simplify 11(x + y) + 7x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
E3

Simplify 9(x + y) + 11x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.
E4

Simplify 9(x + y) + 4x

Need a hint?
  • Distribute first.
  • Then collect x-terms and y-terms separately.