Simplifying · Three Variables · D3

Distribute three terms.

A factor reaches all three terms: 2(x + y + z) = 2x + 2y + 2z. And −(x − y + z) = −x + y − z.

01 / THE IDEA

See it simplify.

Watch it simplify

Distribute three terms

2(x + y + z): the 2 multiplies all three → 2x + 2y + 2z.

1 / 1

2(x + y + z)

Distribute

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

2x + 2y + 2z

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.

Reach them all

a(x + y + z) = ax + ay + az. A leading minus flips all three signs.

Why it works

The factor fans out to every tile.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

4(x + y + z) + 3y

Distribute

Multiply out the brackets — every term inside by the factor in front. → 4x + 4y + 4z + 3y

Group like terms

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

Combine

Add the coefficients within each group. → 4x + 7y + 4z

EX 2medium

4(x + y + z) + 5y

Distribute

Multiply out the brackets — every term inside by the factor in front. → 4x + 4y + 4z + 5y

Group like terms

Gather the terms that share the same variable part. → 4x + (4y + 5y) + 4z

Combine

Add the coefficients within each group. → 4x + 9y + 4z

EX 3hard

5(x + y + z) + 5y

Distribute

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

Group like terms

Gather the terms that share the same variable part. → 5x + (5y + 5y) + 5z

Combine

Add the coefficients within each group. → 5x + 10y + 5z

04 / COMMON TRAPS

Where students slip.

Trap

Missing the third term.

Fix

Multiply all three.

Trap

Sign error under a minus.

Fix

−(x − y + z) = −x + y − z.

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)

Simplify 4(x + y + z) + 3y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 6(x + y + z) + 2y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 4(x + y + z) + 4y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 5(x + y + z) + 3y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Apply

Apply (4)

Simplify 4(x + y + z) + 5y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 3(x + y + z) + 5y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 6(x + y + z) + 6y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 6(x + y + z) + 6y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Extension

Extension (4)

Simplify 5(x + y + z) + 5y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 6(x + y + z) + 7y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 4(x + y + z) + 11y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.

Simplify 5(x + y + z) + 4y

Need a hint?

Multiply the factor by each of the three terms.
Flip all signs if the factor is negative.