Simplifying · Powers · E7

Distribute a variable.

A variable factor distributes and creates powers: x(x + 3) = x² + 3x, and 2x(x − 4) = 2x² − 8x.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute a variable

x(x + 3): x·x = x² and x·3 = 3x → x² + 3x.

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

Distribute

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

x2+3xx^{2} + 3x
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.

Distributing with a variable

x(x + 3) = x·x + x·3 = x² + 3x. The x times x gives a power. 2x(x − 4) = 2x² − 8x.

Why it works

The x fans out and squares where it meets another x.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

x(x + 3)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → x^2 + 3x

EX 2medium

x(x + 5)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → x^2 + 5x

EX 3hard

3x(x + 9)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 3x^2 + 27x

04 / COMMON TRAPS

Where students slip.

Trap

x · x = 2x.

Fix

x · x = x²: the answer is x² + 3x.

Trap

Forgetting to multiply the second term.

Fix

x(x + 3) = x² + 3x, both terms.

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 x(x + 3)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
C2

Simplify x(x + 4)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
C3

Simplify x(x + 3)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
C4

Simplify x(x + 6)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
Apply

Apply (4)

A1

Simplify x(x + 5)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
A2

Simplify 3x(x + 6)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
A3

Simplify 3x(x + 7)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
A4

Simplify x(x + 8)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
Extension

Extension (4)

E1

Simplify 3x(x + 9)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
E2

Simplify 3x(x + 7)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
E3

Simplify 2x(x + 4)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.
E4

Simplify 2x(x + 11)

Need a hint?
  • Multiply the variable into each term.
  • x · x = x², not 2x.