Powers · Add & subtract powers · 2.4

Collect by power.

In a longer expression, only like terms combine. Gather each power separately: the x²’s together, the x’s together. Unlike terms stay apart.

01 / THE IDEA

See it work.

Watch the method

Collect by power

3x² + 2x + x² + 4x = 4x² + 6x.

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3x2+2x+x2+4x3x^{2} + 2x + x^{2} + 4x
1

Group by power

Only terms with the same base AND exponent combine.

3x2+2x+x2+4x3x^{2} + 2x + x^{2} + 4x
2

Combine each group

Add the coefficients within each power; leave unlike terms apart.

=4x2+6x= 4 x^{2} + 6 x
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5.

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— / WHY IT WORKS

The idea underneath.

Sort, then combine

Group terms by their power, add each group’s coefficients, and write the result from highest power down.

Why it works

Sort the x²’s and the x’s into separate piles.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 4x^2 + 4x + 2x^2 + 1x

1

Group by power

Only terms with the same base AND exponent combine. 4x^2 + 4x + 2x^2 + 1x

2

Combine each group

Add the coefficients within each power; leave unlike terms apart. = 6 x^2 + 5 x

EX 2medium

Simplify 4x^2 + 3x + 1x^2 + 4x

1

Group by power

Only terms with the same base AND exponent combine. 4x^2 + 3x + 1x^2 + 4x

2

Combine each group

Add the coefficients within each power; leave unlike terms apart. = 5 x^2 + 7 x

EX 3hard

Simplify 2x^2 + 2x + 4x^2 + 4x

1

Group by power

Only terms with the same base AND exponent combine. 2x^2 + 2x + 4x^2 + 4x

2

Combine each group

Add the coefficients within each power; leave unlike terms apart. = 6 x^2 + 6 x

04 / COMMON TRAPS

Where students slip.

Trap

Combining x² with x.

Fix

Different powers don’t combine.

Trap

Forgetting a term.

Fix

Account for every term in each group.

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 3y^2 + 2y + 4y^2 + 2y

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
C2

Simplify 4x^2 + 1x + 4x^2 + 2x

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
C3

Simplify 2x^2 + 4x + 1x^2 + 4x

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
C4

Simplify 3y^2 + 4y + 1y^2 + 3y

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
Apply

Apply (4)

A1

Simplify 2z^2 + 3z + 4z^2 + 4z

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
A2

Simplify 4y^2 + 2y + 4y^2 + 1y

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
A3

Simplify 4z^2 + 4z + 4z^2 + 2z

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
A4

Simplify 1z^2 + 1z + 1z^2 + 1z

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
Extension

Extension (4)

E1

Simplify 3z^2 + 4z + 1z^2 + 4z

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
E2

Simplify 1z^2 + 4z + 1z^2 + 2z

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
E3

Simplify 1x^2 + 2x + 1x^2 + 4x

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.
E4

Simplify 1x^2 + 1x + 4x^2 + 3x

Need a hint?
  • Group by matching power.
  • Add each group; keep unlike terms separate.