Final answer:
When multiplying the binomials (x-4) and (x+9), you use the FOIL method to get the result of x² + 9x - 4x - 36. After combining like terms, the final simplified expression is x² + 5x - 36.
Step-by-step explanation:
Multiplying the binomials (x-4)(x+9) involves using the FOIL method, which stands for 'First, Outer, Inner, Last'. To illustrate this method, consider drawing a box where you divide it into four sections. Each section of the box represents the product of one term from the first binomial and one term from the second binomial.
Following the FOIL steps:
- First: Multiply the first terms in each binomial: x * x = x².
- Outer: Multiply the outer terms: x * 9 = 9x.
- Inner: Multiply the inner terms: -4 * x = -4x.
- Last: Multiply the last terms in each binomial: -4 * 9 = -36.
Combining these results, we get:
x² + 9x - 4x - 36
Combine like terms (9x and -4x) to obtain the final simplified expression:
x² + 5x - 36