Simplifying · Powers · E4

Collect by power.

Sort a polynomial by power: gather the x²-terms, then the x-terms, then constants. 3x² + 2x + x² + 4x = 4x² + 6x. Write highest power first.

01 / THE IDEA

See it simplify.

Watch it simplify

Collect by power

Collect the x² terms and the x terms separately.

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.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Order by degree

Group x²-terms together and x-terms together. Write the answer from highest power down: 4x² + 6x.

Why it works

Squares in one pile, sticks in another.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5x² + 2x + 3x² + 5x

1

Group like terms

Gather the terms that share the same variable part. → (5x^2 + 3x^2) + (2x + 5x)

2

Combine

Add the coefficients within each group. → 8x^2 + 7x

EX 2medium

7x² + 4x + 6x² + 5x

1

Group like terms

Gather the terms that share the same variable part. → (7x^2 + 6x^2) + (4x + 5x)

2

Combine

Add the coefficients within each group. → 13x^2 + 9x

EX 3hard

8x² + 12x + 9x² + 8x

1

Group like terms

Gather the terms that share the same variable part. → (8x^2 + 9x^2) + (12x + 8x)

2

Combine

Add the coefficients within each group. → 17x^2 + 20x

04 / COMMON TRAPS

Where students slip.

Trap

Mixing x² and x terms.

Fix

Different powers, different piles.

Trap

Writing low power first.

Fix

Convention: highest power first.

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 + 2x + 3x² + 5x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
C2

Simplify 5x² + 2x + 2x² + 3x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
C3

Simplify 6x² + 3x + 4x² + 6x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
C4

Simplify 2x² + 3x + 5x² + 6x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
Apply

Apply (4)

A1

Simplify 7x² + 4x + 6x² + 5x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
A2

Simplify 9x² + 6x + 3x² + 4x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
A3

Simplify 8x² + 4x + 5x² + 4x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
A4

Simplify 6x² + 6x + 9x² + 3x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
Extension

Extension (4)

E1

Simplify 8x² + 12x + 9x² + 8x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
E2

Simplify 12x² + 11x + 9x² + 5x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
E3

Simplify 4x² + 6x + 5x² + 5x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.
E4

Simplify 5x² + 5x + 8x² + 11x

Need a hint?
  • Collect each power separately.
  • Write the highest power first.