Simplifying · Capstone · F1

The full method.

Any expression simplifies the same way: expand the brackets, distribute carefully (watch signs), collect like terms (match variable AND power), and order by degree.

01 / THE IDEA

See it simplify.

Watch it simplify

The full method

Brackets first, distribute, collect, order — every time.

1 / 3
2(x+3)+3x−x2+4x22(x + 3) + 3x - x^2 + 4x^2
1

Distribute

Multiply out the brackets — every term inside by the factor in front.

2x+6+3x−x2+4x22x + 6 + 3x - x^{2} + 4x^{2}
2

Group like terms

Gather the terms that share the same variable part.

(−x2+4x2)+(2x+3x)+6(-x^{2} + 4x^{2}) + (2x + 3x) + 6
3

Combine

Add the coefficients within each group.

3x2+5x+63x^{2} + 5x + 6
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.

The simplifying recipe

1) Expand brackets. 2) Distribute factors (flip signs under a minus). 3) Collect like terms (same variable, same power). 4) Order from highest power down. The pad accepts only the fully simplified form.

Why it works

Open every box, sort every tile, line them up.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

4x + 6y - 3x - 2y

1

Group like terms

Gather the terms that share the same variable part. → (4x - 3x) + (6y - 2y)

2

Combine

Add the coefficients within each group. → x + 4y

EX 2medium

9x² + 9x²

1

Group like terms

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

2

Combine

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

EX 3hard

9x² + 10x + 4x² + 10x

1

Group like terms

Gather the terms that share the same variable part. → (9x^2 + 4x^2) + (10x + 10x)

2

Combine

Add the coefficients within each group. → 13x^2 + 20x

04 / COMMON TRAPS

Where students slip.

Trap

Collecting before distributing.

Fix

Always expand brackets first.

Trap

Combining unlike terms.

Fix

Match the variable AND the power.

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 4x + 6y - 3x - 2y

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
C2

Simplify 6x · 5x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
C3

Simplify 2x · 5x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
C4

Simplify 4x² + 5x + 3x² + 2x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
Apply

Apply (4)

A1

Simplify 9x² + 9x²

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
A2

Simplify 7x² + 7x²

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
A3

Simplify 6x² + 5x + 9x² + 6x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
A4

Simplify 7x² + 9x + 7x² + 4x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
Extension

Extension (4)

E1

Simplify 9x² + 10x + 4x² + 10x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
E2

Simplify 15x + 9y - 5x - 8y

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
E3

Simplify 9x² + 7x + 12x² + 9x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.
E4

Simplify 9x² + 5x + 5x² + 4x

Need a hint?
  • Distribute first, then collect.
  • Match variable and power to combine.