Simplifying · Powers · E3

Combine like powers.

Terms with the same power combine by adding coefficients, keeping the power: 2x² + 5x² = 7x². The exponent does not change.

01 / THE IDEA

See it simplify.

Watch it simplify

Combine like powers

2x² + 5x²: add 2 + 5 = 7, keep x² → 7x².

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2x2+5x22x^2 + 5x^2
1

Group like terms

Gather the terms that share the same variable part.

(2x2+5x2)(2x^{2} + 5x^{2})
2

Combine

Add the coefficients within each group.

7x27x^{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.

Same power, add counts

2x² + 5x² = 7x². You are counting x²-tiles. The exponent stays 2 — you never add the powers.

Why it works

2 square tiles + 5 square tiles = 7 square tiles.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5x² + 6x²

1

Group like terms

Gather the terms that share the same variable part. → (5x^2 + 6x^2)

2

Combine

Add the coefficients within each group. → 11x^2

EX 2medium

8x² + 3x²

1

Group like terms

Gather the terms that share the same variable part. → (8x^2 + 3x^2)

2

Combine

Add the coefficients within each group. → 11x^2

EX 3hard

11x² + 7x²

1

Group like terms

Gather the terms that share the same variable part. → (11x^2 + 7x^2)

2

Combine

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

04 / COMMON TRAPS

Where students slip.

Trap

2x² + 5x² = 7x⁴.

Fix

Add coefficients, keep the power: 7x².

Trap

2x² + 5x² = 7x.

Fix

The power stays 2.

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 5x² + 6x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
C2

Simplify 5x² + 6x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
C3

Simplify 3x² + 6x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
C4

Simplify 2x² + 4x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
Apply

Apply (4)

A1

Simplify 8x² + 3x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
A2

Simplify 8x² + 6x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
A3

Simplify 4x² + 5x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
A4

Simplify 6x² + 4x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
Extension

Extension (4)

E1

Simplify 11x² + 7x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
E2

Simplify 5x² + 4x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
E3

Simplify 9x² + 8x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.
E4

Simplify 12x² + 7x²

Need a hint?
  • Add the coefficients.
  • Keep the exponent the same.