The Distributive Property
Multiply a number by a bracket: 2(x + 3) = 2x + 6. Watch the magic of distribution.
Equation
y = 1*(x + 1)
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |
| 5 | 6 |
What this lesson covers
What you do
You shape the function y = n*(x + a) and watch the graph answer.
Challenges to clear
- Build 2*(x + 3): set n = 2 and a = 3. Check that x = 2 gives 2*(2+3) = 10.
- Distribute it: 2x + 6 at x = 4 is 8 + 6 = 14 — confirm the table agrees.
- Build your own product: n(x + 4). Slide a to 4 first.
- Now slide n until x = 2 gives 18. Distributed, that is 3x + 12 — the multiplier reaches BOTH terms inside.
Check yourself
Why is 2*(x + 3) equal to 2x + 6 and NOT 2x + 3?
What is the specific mistake in the 'wrong' expansion 2*(x + 3) = 2x + 3?
- Because the 2 must multiply every term inside the parentheses, including the 3. — correct
- Because x and 3 are added first, so the 2 only applies to the sum.
- Because 2 times 3 is 3, not 6.
- Because the 2 only multiplies the variable x, not the constant.
- It forgot to distribute the 2 to the 3. — correct
- It added 2 to x instead of multiplying.
- It multiplied 2 by 3 to get 9.
- It subtracted 3 instead of adding it.
Think about it
- 2*(x + 3) means: multiply BOTH the x and the 3 by 2. What is 2*(4 + 3)?