Simplifying · Powers · E8

Powers mastery.

Pull the power rules together: combine like powers (add coefficients), multiply (add exponents), and distribute variable factors.

01 / THE IDEA

See it simplify.

Watch it simplify

Powers mastery

Watch whether you are adding terms or multiplying them.

1 / 1
3x⋅2x3x\cdot 2x
1

Simplify

Multiply out and write it in simplest form.

6x26x^{2}
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.

Two different "adds"

Combining like terms adds COEFFICIENTS (2x² + 5x² = 7x²). Multiplying same bases adds EXPONENTS (x² · x³ = x⁵). Know which you are doing.

Why it works

Side by side vs multiplied together.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

3x² + 6x²

1

Group like terms

Gather the terms that share the same variable part. → (3x^2 + 6x^2)

2

Combine

Add the coefficients within each group. → 9x^2

EX 2medium

x(x + 8)

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → x^2 + 8x

EX 3hard

4x² + 11x + 12x² + 11x

1

Group like terms

Gather the terms that share the same variable part. → (4x^2 + 12x^2) + (11x + 11x)

2

Combine

Add the coefficients within each group. → 16x^2 + 22x

04 / COMMON TRAPS

Where students slip.

Trap

Adding exponents when combining like terms.

Fix

2x² + 5x² = 7x², not 7x⁴.

Trap

Multiplying exponents when multiplying.

Fix

x² · x³ = x⁵ (add), not x⁶.

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 3x² + 6x²

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
C2

Simplify 4x · 5x

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
C3

Simplify 6x · 2x

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
C4

Simplify x(x + 6)

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
Apply

Apply (4)

A1

Simplify x(x + 8)

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
A2

Simplify 6x² + 3x²

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
A3

Simplify 7x · 3x

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
A4

Simplify 3x(x + 7)

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
Extension

Extension (4)

E1

Simplify 4x² + 11x + 12x² + 11x

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
E2

Simplify x(x + 10)

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
E3

Simplify 6x² + 10x²

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.
E4

Simplify x(x + 5)

Need a hint?
  • Adding terms: add coefficients.
  • Multiplying: add exponents.