Simplifying · One Variable · B11

Distribute then collect.

Real expressions need both steps: distribute the brackets first, then collect like terms. 2(x + 4) + 3x = 2x + 8 + 3x = 5x + 8.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute then collect

2(x + 4) + 3x: expand to 2x + 8 + 3x, then collect → 5x + 8.

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2(x+4)+3x2(x + 4) + 3x
1

Distribute

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

2x+8+3x2x + 8 + 3x
2

Group like terms

Gather the terms that share the same variable part.

(2x+3x)+8(2x + 3x) + 8
3

Combine

Add the coefficients within each group.

5x+85x + 8
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.

Two steps in order

Brackets must be expanded before you can collect. 5x − 2(x − 1) = 5x − 2x + 2 = 3x + 2 — note the minus distributes first.

Why it works

Open the boxes, then sort the tiles.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

3(x + 3) + 2x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 3x + 9 + 2x

2

Group like terms

Gather the terms that share the same variable part. → (3x + 2x) + 9

3

Combine

Add the coefficients within each group. → 5x + 9

EX 2medium

7(x + 9) + 5x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 7x + 63 + 5x

2

Group like terms

Gather the terms that share the same variable part. → (7x + 5x) + 63

3

Combine

Add the coefficients within each group. → 12x + 63

EX 3hard

7(x + 11) + 5x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 7x + 77 + 5x

2

Group like terms

Gather the terms that share the same variable part. → (7x + 5x) + 77

3

Combine

Add the coefficients within each group. → 12x + 77

04 / COMMON TRAPS

Where students slip.

Trap

Collecting before distributing.

Fix

Expand the bracket first, then combine.

Trap

5x − 2(x − 1) = 5x − 2x − 2.

Fix

The −2 hits the −1 too: + 2, giving 3x + 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 3(x + 3) + 2x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
C2

Simplify 4(x + 3) + 6x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
C3

Simplify 3(x + 6) + 3x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
C4

Simplify 6(x + 2) + 3x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
Apply

Apply (4)

A1

Simplify 7(x + 9) + 5x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
A2

Simplify 4(x + 4) + 8x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
A3

Simplify 5(x + 8) + 4x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
A4

Simplify 6(x + 8) + 4x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
Extension

Extension (4)

E1

Simplify 7(x + 11) + 5x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
E2

Simplify 8(x + 5) + 8x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
E3

Simplify 10(x + 8) + 8x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.
E4

Simplify 11(x + 11) + 9x

Need a hint?
  • Distribute every bracket first.
  • Then add up the like terms.