Simplifying · One Variable · B9

Distribute over a sum.

To remove a bracket, multiply the factor by every term inside: 3(x + 2) = 3x + 6. Miss a term and the answer is wrong.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute over a sum

3(x + 2): 3·x = 3x and 3·2 = 6, so 3x + 6.

1 / 1
3(x+2)3(x + 2)
1

Distribute

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

3x+63x + 6
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.

The distributive law

a(b + c) = ab + ac. The outside factor reaches every inside term. 3(x + 2) = 3x + 6.

Why it works

3 rows of (x + 2) is 3 xs and 3 twos.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

3(x - 6)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 3x - 18

EX 2medium

7(x + 6)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 7x + 42

EX 3hard

7(x + 4)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 7x + 28

04 / COMMON TRAPS

Where students slip.

Trap

3(x + 2) = 3x + 2 (only the first term).

Fix

Multiply BOTH: 3x + 6.

Trap

3(x + 2) = 3x · 6.

Fix

Distribute as a sum: 3x + 6.

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 3(x - 6)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
C2

Simplify 4(x - 2)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
C3

Simplify 4(x + 2)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
C4

Simplify 4(x + 5)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
Apply

Apply (4)

A1

Simplify 7(x + 6)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
A2

Simplify 5(x - 6)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
A3

Simplify 8(x + 8)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
A4

Simplify 7(x - 3)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
Extension

Extension (4)

E1

Simplify 7(x + 4)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
E2

Simplify 5(x + 7)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
E3

Simplify 8(x - 4)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.
E4

Simplify 9(x + 4)

Need a hint?
  • Multiply the outside number by each inside term.
  • Do not forget the second term.