Simplifying · One Variable · B10

Distribute with a minus.

A negative factor flips the sign of every term it distributes over. −(x + 5) = −x − 5, and −2(x − 3) = −2x + 6. This is the top sign-error spot.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute with a minus

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

1 / 1
−2(x−3)-2(x - 3)
1

Distribute

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

−2x+6-2x + 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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… =
— / WHY IT WORKS

The idea underneath.

Signs under distribution

Multiply signs too. −(x + 5) = −x − 5. −2(x − 3): −2 times −3 is +6. Track each sign carefully.

Why it works

A minus in front turns every inside term around.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

-2(x + 2)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → -2x - 4

EX 2medium

-7(x + 7)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → -7x - 49

EX 3hard

-8(x - 12)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → -8x + 96

04 / COMMON TRAPS

Where students slip.

Trap

−(x + 5) = −x + 5.

Fix

Both flip: −x − 5.

Trap

−2(x − 3) = −2x − 6.

Fix

Minus times minus is plus: −2x + 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 -2(x + 2)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
C2

Simplify -4(x - 3)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
C3

Simplify -5(x - 6)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
C4

Simplify -6(x + 2)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
Apply

Apply (4)

A1

Simplify -7(x + 7)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
A2

Simplify -3(x + 6)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
A3

Simplify -9(x - 4)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
A4

Simplify -2(x + 3)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
Extension

Extension (4)

E1

Simplify -8(x - 12)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
E2

Simplify -6(x - 11)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
E3

Simplify -4(x - 10)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.
E4

Simplify -2(x - 8)

Need a hint?
  • Multiply the signs as well as the numbers.
  • Minus times minus is plus.