Simplifying · Powers · E2

x² and x are not alike.

x² and x are unlike terms — different powers — so x² + x cannot be combined. Only terms with the same variable AND the same power are alike.

01 / THE IDEA

See it simplify.

Watch it simplify

x² and x are not alike

x² + x stays as is — the powers differ.

1 / 2
3x2+2x+x2+4x3x^2 + 2x + x^2 + 4x
1

Group like terms

Gather the terms that share the same variable part.

(3x2+x2)+(2x+4x)(3x^{2} + x^{2}) + (2x + 4x)
2

Combine

Add the coefficients within each group.

4x2+6x4x^{2} + 6x
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.

Power matters

Like terms must match the variable and the exponent. x² and x are different kinds, like x and a number were. x² + 3x is already simplified.

Why it works

A square tile and a stick tile are different shapes.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

4x² + 2x + 4x² + 2x

1

Group like terms

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

2

Combine

Add the coefficients within each group. → 8x^2 + 4x

EX 2medium

4x² + 3x + 3x² + 7x

1

Group like terms

Gather the terms that share the same variable part. → (4x^2 + 3x^2) + (3x + 7x)

2

Combine

Add the coefficients within each group. → 7x^2 + 10x

EX 3hard

6x² + 6x + 12x² + 4x

1

Group like terms

Gather the terms that share the same variable part. → (6x^2 + 12x^2) + (6x + 4x)

2

Combine

Add the coefficients within each group. → 18x^2 + 10x

04 / COMMON TRAPS

Where students slip.

Trap

x² + x = x³.

Fix

You cannot combine unlike powers.

Trap

x² + x = 2x².

Fix

They do not combine at all.

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 4x² + 2x + 4x² + 2x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
C2

Simplify 6x² + 3x + 3x² + 3x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
C3

Simplify 3x² + 2x + 5x² + 5x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
C4

Simplify 5x² + 4x + 5x² + 6x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
Apply

Apply (4)

A1

Simplify 4x² + 3x + 3x² + 7x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
A2

Simplify 4x² + 3x + 5x² + 5x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
A3

Simplify 6x² + 7x + 5x² + 6x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
A4

Simplify 4x² + 3x + 3x² + 3x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
Extension

Extension (4)

E1

Simplify 6x² + 6x + 12x² + 4x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
E2

Simplify 10x² + 10x + 8x² + 6x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
E3

Simplify 8x² + 12x + 9x² + 8x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.
E4

Simplify 4x² + 11x + 10x² + 5x

Need a hint?
  • Match the power as well as the letter.
  • Different powers do not combine.