Track many brackets
Distribute 3(x + y) and 2(y + z), then gather: xs 3 + 1 = 4, ys 3 + 2 = 5, zs 2. Result 4x + 5y + 2z.
Why it works
Open all the boxes, then sort.
Simplifying · Three Variables · D4
Big mixed brackets.
Several brackets at once: distribute each, then collect all three letters. 3(x + y) + 2(y + z) + x = 4x + 5y + 2z.
See it simplify.
Watch it simplify
Big mixed brackets
Expand both brackets, then collect x, y, z.
1
Distribute
Multiply out the brackets — every term inside by the factor in front.
2
Group like terms
Gather the terms that share the same variable part.
3
Combine
Add the coefficients within each group.
Practice until it feels automatic.
Your turn
Simplify it.
Type the simplest form (e.g. 6x + 5). Use ^ for powers.
streak 0
best 0
… =
The idea underneath.
From easy to tricky.
3(x + y) + 3(y + z) + 4x
1
Distribute
Multiply out the brackets — every term inside by the factor in front. → 3x + 3y + 3y + 3z + 4x
2
Group like terms
Gather the terms that share the same variable part. → (3x + 4x) + (3y + 3y) + 3z
3
Combine
Add the coefficients within each group. → 7x + 6y + 3z
7(x + y) + 9(y + z) + 7x
1
Distribute
Multiply out the brackets — every term inside by the factor in front. → 7x + 7y + 9y + 9z + 7x
2
Group like terms
Gather the terms that share the same variable part. → (7x + 7x) + (7y + 9y) + 9z
3
Combine
Add the coefficients within each group. → 14x + 16y + 9z
11(x + y) + 5(y + z) + 11x
1
Distribute
Multiply out the brackets — every term inside by the factor in front. → 11x + 11y + 5y + 5z + 11x
2
Group like terms
Gather the terms that share the same variable part. → (11x + 11x) + (11y + 5y) + 5z
3
Combine
Add the coefficients within each group. → 22x + 16y + 5z
Where students slip.
Trap
Forgetting a bracket.
Fix
Distribute every bracket before collecting.
Trap
Mixing the ys from different brackets wrongly.
Fix
Add all y-terms together: 3y + 2y = 5y.
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 + y) + 3(y + z) + 4x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
C2
Simplify 6(x + y) + 4(y + z) + 4x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
C3
Simplify 2(x + y) + 2(y + z) + 3x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
C4
Simplify 6(x + y) + 2(y + z) + 6x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
Apply
Apply (4)
A1
Simplify 7(x + y) + 9(y + z) + 7x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
A2
Simplify 4(x + y) + 9(y + z) + 4x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
A3
Simplify 3(x + y) + 8(y + z) + 3x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
A4
Simplify 8(x + y) + 4(y + z) + 9x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
Extension
Extension (4)
E1
Simplify 11(x + y) + 5(y + z) + 11x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
E2
Simplify 7(x + y) + 10(y + z) + 4x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
E3
Simplify 5(x + y) + 9(y + z) + 7x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.
E4
Simplify 12(x + y) + 7(y + z) + 7x
Need a hint?
- Distribute each bracket first.
- Then collect x, y, and z.