The Correct Answer and Explanation is:
Correct Answer:
6x² + 23x – 18
Explanation:
The problem requires us to multiply two binomials, (3x – 2) and (2x + 9), and express the result as a trinomial, which is a polynomial with three terms. A common and reliable method for multiplying two binomials is the FOIL method. FOIL is an acronym that stands for First, Outer, Inner, and Last, ensuring that each term in the first binomial is multiplied by each term in the second binomial.
Let’s apply the FOIL method step by step to the expression (3x – 2)(2x + 9):
- First: Multiply the first term of each binomial.
(3x) * (2x) = 6x² - Outer: Multiply the two outermost terms of the expression.
(3x) * (+9) = 27x - Inner: Multiply the two innermost terms of the expression.
(-2) * (2x) = -4x
It is crucial to carry the negative sign with the 2. - Last: Multiply the last term of each binomial.
(-2) * (+9) = -18
After completing these four multiplications, we combine the resulting terms into a single expression:
6x² + 27x – 4x – 18
The final step is to simplify this expression by combining like terms. Like terms are terms that contain the same variable raised to the same power. In this expression, the like terms are 27x and -4x. We can combine them by performing the indicated subtraction:
27x – 4x = 23x
The other terms, 6x² and -18, do not have any other like terms, so they remain as they are. By substituting the combined term back into the expression, we get our final answer.
The simplified expression is 6x² + 23x – 18. This is a trinomial because it has three distinct terms: a quadratic term (6x²), a linear term (23x), and a constant term (-18).
