Multiply the 2 binomials using FOIL and the box method:
(2x + 6)(3x - 9)
Define FOIL Formula:
First-Outside-Inside-Last:
(a + b)(c + d) = (a * c) + (b * c) + (a * d) + (b * d)
Set our FOIL values:
a = 2x, b = 6, c = 3x, and d = -9
Evaluate:
(2x + 6)(3x - 9) = (2x * 3x) + (6 * 3x) + (2x * -9) + (6 * -9)
(2x + 6)(3x - 9) = 6x2 + 18 - 18x - 54
FOIL Box Method
Write the first 2 terms across the top and the next 2 terms horizontally
| 2x | 6 | |
| 3x | ||
| -9 |
Multiply each top row term by the respective left column term
| 2x | 6 | |
| 3x | 2x * 3x | 6 * 3x |
| -9 | 2x * -9 | 6 * -9 |
(2x + 6)(3x - 9) = (2x * 3x) + (6 * 3x) + (2x * -9) + (6 * -9)
(2x + 6)(3x - 9) = 6x2 + 18 - 18x - 54
Final Answer
6x2 - 54
