Final answer:
The expression 3(2x + 3)(3x² + x - 9) simplifies to 18x³ + 33x² + 9x - 81, using the FOIL method and then multiplying by 3.
Step-by-step explanation:
The student has asked to simplify the expression 3(2x + 3)(3x² + x - 9). To simplify this expression, we will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), which is a technique for multiplying two binomials. First, multiply the binomials (2x + 3) and (3x² + x - 9), and then multiply the resulting polynomial by 3.
Let's start by multiplying the binomials:
- First: 2x × 3x² = 6x³
- Outer: 2x × x = 2x²
- Inner: 3 × 3x² = 9x²
- Last: 3 × x = 3x
- Last: 3 × -9 = -27
Add up the like terms from the multiplication: 6x³ + (2x² + 9x²) + 3x - 27 = 6x³ + 11x² + 3x - 27.
Finally, multiply by 3:
- 3 × 6x³ = 18x³
- 3 × 11x² = 33x²
- 3 × 3x = 9x
- 3 × -27 = -81
Thus, the simplified form of the expression is 18x³ + 33x² + 9x - 81.