Simplifying · Three Variables · D2

Bigger collections.

Longer expressions, same rule: combine each letter with its signs. 2x − y + 3z − x + 4y = x + 3y + 3z.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

2x
-y
3z
-x
4y

All the terms, mixed up.

Watch it simplify

Bigger collections

Go letter by letter, keeping signs.

1 / 2
2x−y+3z−x+4y2x - y + 3z - x + 4y
1

Group like terms

Gather the terms that share the same variable part.

(2x−x)+(−y+4y)+3z(2x - x) + (-y + 4y) + 3z
2

Combine

Add the coefficients within each group.

x+3y+3zx + 3y + 3z
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

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

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Stay organised

Scan once per letter. xs: 2 − 1 = 1. ys: −1 + 4 = 3. zs: 3. Result x + 3y + 3z.

Why it works

Three number lines running in parallel.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

9x + 4y - 8x + 3z + 6y

1

Group like terms

Gather the terms that share the same variable part. → (9x - 8x) + (4y + 6y) + 3z

2

Combine

Add the coefficients within each group. → x + 10y + 3z

EX 2medium

6x + 4y - 5x + 9z + 4y

1

Group like terms

Gather the terms that share the same variable part. → (6x - 5x) + (4y + 4y) + 9z

2

Combine

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

EX 3hard

15x + 10y - 11x + 7z + 12y

1

Group like terms

Gather the terms that share the same variable part. → (15x - 11x) + (10y + 12y) + 7z

2

Combine

Add the coefficients within each group. → 4x + 22y + 7z

04 / COMMON TRAPS

Where students slip.

Trap

Losing a sign mid-scan.

Fix

Each term keeps its sign.

Trap

Combining across letters.

Fix

Stay within one letter at a time.

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 9x + 4y - 8x + 3z + 6y

Need a hint?
  • One letter at a time.
  • Keep every sign.
C2

Simplify 7x + 5y - 2x + 6z + 5y

Need a hint?
  • One letter at a time.
  • Keep every sign.
C3

Simplify 7x + 5y - 4x + 2z + 4y

Need a hint?
  • One letter at a time.
  • Keep every sign.
C4

Simplify 9x + 6y - 6x + 5z + 2y

Need a hint?
  • One letter at a time.
  • Keep every sign.
Apply

Apply (4)

A1

Simplify 6x + 4y - 5x + 9z + 4y

Need a hint?
  • One letter at a time.
  • Keep every sign.
A2

Simplify 8x + 4y - 4x + 9z + 4y

Need a hint?
  • One letter at a time.
  • Keep every sign.
A3

Simplify 10x + 4y - 8x + 5z + 3y

Need a hint?
  • One letter at a time.
  • Keep every sign.
A4

Simplify 8x + 5y - 6x + 4z + 6y

Need a hint?
  • One letter at a time.
  • Keep every sign.
Extension

Extension (4)

E1

Simplify 15x + 10y - 11x + 7z + 12y

Need a hint?
  • One letter at a time.
  • Keep every sign.
E2

Simplify 15x + 11y - 8x + 5z + 5y

Need a hint?
  • One letter at a time.
  • Keep every sign.
E3

Simplify 10x + 7y - 5x + 9z + 11y

Need a hint?
  • One letter at a time.
  • Keep every sign.
E4

Simplify 14x + 12y - 5x + 10z + 7y

Need a hint?
  • One letter at a time.
  • Keep every sign.