Simplifying · Two Variables · C6

The product xy.

Multiplying different variables makes a new term: x · y = xy. And 3x · 2y = 6xy. The term xy is its own kind — not like x, not like y, and xy = yx.

01 / THE IDEA

See it simplify.

Watch it simplify

The product xy

3x · 2y: multiply 3·2 = 6 and stick the letters together → 6xy.

1 / 1
3x⋅2y3x\cdot 2y
1

Simplify

Multiply out and write it in simplest form.

6xy6xy
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.

A combined variable

Multiplying x and y gives xy (order does not matter: xy = yx). 3x · 2y = 6xy. xy is unlike x and unlike y.

Why it works

An x-by-y rectangle tile — a new shape.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

4x · 2y

1

Simplify

Multiply out and write it in simplest form. → 8xy

EX 2medium

6x · 3y

1

Simplify

Multiply out and write it in simplest form. → 18xy

EX 3hard

7x · 4y

1

Simplify

Multiply out and write it in simplest form. → 28xy

04 / COMMON TRAPS

Where students slip.

Trap

x · y = x + y.

Fix

Multiplication gives xy, not a sum.

Trap

Treating xy like an x-term.

Fix

xy is its own kind of term.

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 4x · 2y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
C2

Simplify 6x · 6y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
C3

Simplify 2x · 4y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
C4

Simplify 3x · 2y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
Apply

Apply (4)

A1

Simplify 6x · 3y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
A2

Simplify 5x · 5y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
A3

Simplify 4x · 4y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
A4

Simplify 9x · 8y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
Extension

Extension (4)

E1

Simplify 7x · 4y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
E2

Simplify 12x · 9y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
E3

Simplify 11x · 11y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.
E4

Simplify 4x · 6y

Need a hint?
  • Multiply the coefficients; join the letters.
  • xy is a new term, and xy = yx.