Simplifying · Two Variables · C1

Different letters.

Different letters are different unknowns. 3x + 2y cannot be combined — they are unlike terms, just like x-terms and numbers were.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

3x
2y
5x

All the terms, mixed up.

Watch it simplify

Different letters

3x and 2y are different kinds, so 3x + 2y stays as is.

1 / 2
3x+2y+5x3x + 2y + 5x
1

Group like terms

Gather the terms that share the same variable part.

(3x+5x)+2y(3x + 5x) + 2y
2

Combine

Add the coefficients within each group.

8x+2y8x + 2y
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.

Two unknowns

x and y stand for different numbers. 3x + 2y is already simplified. Combining them into 5xy or 5 is wrong.

Why it works

Apples and oranges again — different fruit.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5x + 6y + 2x + 4y

1

Group like terms

Gather the terms that share the same variable part. → (5x + 2x) + (6y + 4y)

2

Combine

Add the coefficients within each group. → 7x + 10y

EX 2medium

9x + 7y + 7x + 6y

1

Group like terms

Gather the terms that share the same variable part. → (9x + 7x) + (7y + 6y)

2

Combine

Add the coefficients within each group. → 16x + 13y

EX 3hard

10x + 6y + 4x + 12y

1

Group like terms

Gather the terms that share the same variable part. → (10x + 4x) + (6y + 12y)

2

Combine

Add the coefficients within each group. → 14x + 18y

04 / COMMON TRAPS

Where students slip.

Trap

3x + 2y = 5xy.

Fix

Different letters do not merge: leave 3x + 2y.

Trap

3x + 2y = 5.

Fix

You cannot add unlike terms.

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 5x + 6y + 2x + 4y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
C2

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

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
C3

Simplify 2x + 4y + 3x + 3y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
C4

Simplify 3x + 6y + 2x + 6y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
Apply

Apply (4)

A1

Simplify 9x + 7y + 7x + 6y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
A2

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

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
A3

Simplify 7x + 5y + 4x + 7y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
A4

Simplify 7x + 5y + 3x + 7y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
Extension

Extension (4)

E1

Simplify 10x + 6y + 4x + 12y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
E2

Simplify 6x + 12y + 5x + 5y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
E3

Simplify 10x + 6y + 5x + 11y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.
E4

Simplify 4x + 5y + 11x + 8y

Need a hint?
  • x-terms and y-terms are different kinds.
  • Only combine matching letters.