Simplifying · One Variable · B8

Multiply a number by a term.

Multiplying a number by a term multiplies the coefficient. 4 · 3x = 12x. The variable comes along unchanged (no powers yet).

01 / THE IDEA

See it simplify.

Watch it simplify

Multiply a number by a term

4 · 3x means four lots of 3x = 12x.

1 / 1
4⋅3x4\cdot 3x
1

Simplify

Multiply out and write it in simplest form.

12x12x
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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best 0
… =
— / WHY IT WORKS

The idea underneath.

Scaling a term

4 · 3x = (4 · 3)x = 12x. You are scaling the count. 5 · x = 5x.

Why it works

4 copies of "3 x-tiles" is 12 x-tiles.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5 · 2x

1

Simplify

Multiply out and write it in simplest form. → 10x

EX 2medium

9 · 9x

1

Simplify

Multiply out and write it in simplest form. → 81x

EX 3hard

12 · 4x

1

Simplify

Multiply out and write it in simplest form. → 48x

04 / COMMON TRAPS

Where students slip.

Trap

4 · 3x = 12 (losing the x).

Fix

Keep the variable: 12x.

Trap

4 · 3x = 7x (adding instead).

Fix

Multiply the coefficients: 12x.

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 5 · 2x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
C2

Simplify 5 · 6x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
C3

Simplify 2 · 4x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
C4

Simplify 6 · 6x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
Apply

Apply (4)

A1

Simplify 9 · 9x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
A2

Simplify 3 · 4x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
A3

Simplify 6 · 9x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
A4

Simplify 5 · 3x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
Extension

Extension (4)

E1

Simplify 12 · 4x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
E2

Simplify 9 · 9x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
E3

Simplify 6 · 5x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.
E4

Simplify 9 · 10x

Need a hint?
  • Multiply the numbers in front.
  • The variable stays a single x.