Simplifying · Two Variables · C7

Two-variable mastery.

Bring it together: distribute, then collect each letter, keeping signs — across x, y, and products.

01 / THE IDEA

See it simplify.

Watch it simplify

Two-variable mastery

Distribute, collect x and y separately, keep signs.

1 / 3
2(x+y)+3x−y2(x + y) + 3x - y
1

Distribute

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

2x+2y+3x−y2x + 2y + 3x - y
2

Group like terms

Gather the terms that share the same variable part.

(2x+3x)+(2y−y)(2x + 3x) + (2y - y)
3

Combine

Add the coefficients within each group.

5x+y5x + y
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-variable method

Expand → collect xs → collect ys → collect any xy → keep signs.

Why it works

Sort every tile into its colour pile.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

6x + 2y - 2x - 2y

1

Group like terms

Gather the terms that share the same variable part. → (6x - 2x) + (2y - 2y)

2

Combine

Add the coefficients within each group. → 4x

EX 2medium

4x + 3y + 5x + 5y

1

Group like terms

Gather the terms that share the same variable part. → (4x + 5x) + (3y + 5y)

2

Combine

Add the coefficients within each group. → 9x + 8y

EX 3hard

6x + 10y - 5x - 4y

1

Group like terms

Gather the terms that share the same variable part. → (6x - 5x) + (10y - 4y)

2

Combine

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

04 / COMMON TRAPS

Where students slip.

Trap

Merging unlike letters.

Fix

x, y and xy are three different kinds.

Trap

Sign slips.

Fix

Carry every sign through.

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 6x + 2y - 2x - 2y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
C2

Simplify 4x + 2y - 3x - 5y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
C3

Simplify 2(x + y) + 5x

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
C4

Simplify 2(x + y) + 5x

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
Apply

Apply (4)

A1

Simplify 4x + 3y + 5x + 5y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
A2

Simplify 3x + 3y + 5x + 5y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
A3

Simplify 3x + 4y + 3x + 6y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
A4

Simplify 6(x + y) + 9x

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
Extension

Extension (4)

E1

Simplify 6x + 10y - 5x - 4y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
E2

Simplify 14x + 8y - 7x - 4y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
E3

Simplify 7(x + y) + 7x

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.
E4

Simplify 8x + 4y + 7x + 8y

Need a hint?
  • Distribute, then collect each letter.
  • Keep x, y, and xy apart.