The Distributive Property: Don't Forget the Last Term!
Watch how a monomial multiplies every single term inside the bracket.
Equation
y = 4*x*(3*x + 2) - (12*x^2 + 0*x)
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | 8 |
| 2 | 16 |
| 3 | 24 |
What this lesson covers
What you do
You shape the function y = 4*x*(3*x + 2) - (12*x^2 + k*x) and watch the graph answer.
Challenges to clear
- 4x multiplies EVERY term: 4x · 2 = 8x. Slide k to 8 — the difference is 0 at x = 2.
- Don't forget the last term! Still 0 at x = 3.
- Distribute 5x over (2x + 3). The x² term is 5 × 2 — slide m to 10.
- Now the second term, the one people forget: 5x × 3. Slide k until the difference is 0 at x = 2.
Check yourself
What is the most common mistake when expanding 4x(3x + 2)?
What is 4x × (3x + 2)?
- Multiplying only the first term: writing 12x² + 2 instead of 12x² + 8x. — correct
- Adding instead of multiplying the coefficients.
- Forgetting the x in 4x.
- Writing the answer in the wrong order.
- 12x² + 8x — correct
- 12x² + 2
- 7x + 2
- 12x + 8x²
Think about it
- What is 4x × 2?