Simplifying · Three Variables · D1

Three letters.

Three variables work the same way: collect x, y, and z each separately. x + 2y + 3z + 4x = 5x + 2y + 3z.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

x
2y
3z
4x

All the terms, mixed up.

Watch it simplify

Three letters

x + 2y + 3z + 4x: xs → 5x; y and z carry through.

1 / 2
x+2y+3z+4xx + 2y + 3z + 4x
1

Group like terms

Gather the terms that share the same variable part.

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

Combine

Add the coefficients within each group.

5x+2y+3z5x + 2y + 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.

Three piles

Sweep up xs, then ys, then zs. Order the answer x, y, z.

Why it works

Three colour piles instead of two.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

3x + 5y + 5z + 5x

1

Group like terms

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

2

Combine

Add the coefficients within each group. → 8x + 5y + 5z

EX 2medium

4x + 8y + 8z + 9x

1

Group like terms

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

2

Combine

Add the coefficients within each group. → 13x + 8y + 8z

EX 3hard

8x + 5y + 5z + 8x

1

Group like terms

Gather the terms that share the same variable part. → (8x + 8x) + 5y + 5z

2

Combine

Add the coefficients within each group. → 16x + 5y + 5z

04 / COMMON TRAPS

Where students slip.

Trap

Mixing any two letters.

Fix

Each letter stays separate.

Trap

Dropping a single z.

Fix

Carry every term 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 3x + 5y + 5z + 5x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
C2

Simplify 5x + 6y + 3z + 5x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
C3

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

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
C4

Simplify 4x + 4y + 5z + 4x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
Apply

Apply (4)

A1

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

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
A2

Simplify 9x + 5y + 8z + 6x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
A3

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

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
A4

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

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
Extension

Extension (4)

E1

Simplify 8x + 5y + 5z + 8x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
E2

Simplify 11x + 11y + 10z + 9x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
E3

Simplify 7x + 12y + 5z + 6x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.
E4

Simplify 8x + 7y + 6z + 4x

Need a hint?
  • Collect x, then y, then z.
  • Order the answer x, y, z.