Simplifying · Two Variables · C4

Distribute over two.

Distribution reaches both letters: 2(x + y) = 2x + 2y, and 2(3x − y) = 6x − 2y.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute over two

2(x + y): 2·x and 2·y → 2x + 2y.

1 / 1
2(3x−y)2(3x - y)
1

Distribute

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

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.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Both letters get the factor

a(x + y) = ax + ay. 2(3x − y) = 6x − 2y. Every inside term, every letter.

Why it works

The 2 fans out to each tile inside.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

6(2x - 6y)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 12x - 36y

EX 2medium

8(3x + 4y)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 24x + 32y

EX 3hard

10(12x - 11y)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 120x - 110y

04 / COMMON TRAPS

Where students slip.

Trap

2(x + y) = 2x + y.

Fix

Both: 2x + 2y.

Trap

Sign slip on a subtracted term.

Fix

2(3x − y) = 6x − 2y.

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 6(2x - 6y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
C2

Simplify 5(4x - 3y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
C3

Simplify 2(5x + 4y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
C4

Simplify 3(6x - 6y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
Apply

Apply (4)

A1

Simplify 8(3x + 4y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
A2

Simplify 3(9x - 4y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
A3

Simplify 9(3x - 5y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
A4

Simplify 9(5x - 9y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
Extension

Extension (4)

E1

Simplify 10(12x - 11y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
E2

Simplify 10(10x + 12y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
E3

Simplify 6(8x - 6y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.
E4

Simplify 8(5x + 7y)

Need a hint?
  • Multiply the factor into each term.
  • Both letters get multiplied.