Multiply the binomials: (x + 3)(2x - 5)
Responses
A	2
 + x - 152 x 2 + x - 15
B	2
 - 11x - 152 x 2 - 11x - 15
C	2
 - 6x + 152 x 2 - 6x + 15
D	2
 + 3x + 15

Let's multiply the binomials \( (x + 3)(2x - 5) \).

We use the distributive property (FOIL method) to multiply the terms:

\[
(x + 3)(2x - 5) = x(2x) + x(-5) + 3(2x) + 3(-5)
\]

Simplifying each term:

\[
x(2x) = 2x^2
\]
\[
x(-5) = -5x
\]
\[
3(2x) = 6x
\]
\[
3(-5) = -15
\]

Now, combine like terms:

\[
2x^2 - 5x + 6x - 15 = 2x^2 + x - 15
\]

Thus, the product is \( 2x^2 + x - 15 \).

The correct response is **B: \( 2x^2 - 11x - 15 \)**.

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Do you want more details or have any questions about this?  
Here are 5 related questions:
1. How do you multiply polynomials with more than two terms?
2. What is the FOIL method, and when can it be used?
3. How do you handle the distributive property in algebra?
4. How do you factor the expression \( 2x^2 + x - 15 \)?
5. What is the difference between binomial and trinomial expressions?

**Tip**: When multiplying binomials, always ensure to combine like terms carefully after applying the distributive property.

Learn how to multiply binomials like (x + 3)(2x - 5) using the FOIL method. This step-by-step guide covers key algebraic concepts, including the distributive property and how to combine like terms. Suitable for students in Grades 8-10.

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