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To multiply and simplify the expression \( (2x - 3y - 6)(5x + 3y) \), we'll use the distributive property, also known as the FOIL method for binomials. Let's go through each step:

1. **First**: Multiply the first terms in each binomial:
   \[
   2x \cdot 5x = 10x^2
   \]

2. **Outer**: Multiply the outer terms in each binomial:
   \[
   2x \cdot 3y = 6xy
   \]

3. **Inner**: Multiply the inner terms in each binomial:
   \[
   -3y \cdot 5x = -15yx
   \]

4. **Last**: Multiply the last terms in each binomial:
   \[
   -3y \cdot 3y = -9y^2
   \]

5. **Constant term with \(x\)**: Multiply \(-6\) with \(5x\) and \(3y\):
   \[
   -6 \cdot 5x = -30x, \quad -6 \cdot 3y = -18y
   \]

Now, combining all these:
\[
10x^2 + (6xy

Multiply and simplify the expression (2x - 3y - 6)(5x + 3y).

Explore how to simplify the polynomial expression (2x - 3y - 6)(5x + 3y) using the FOIL method. This detailed guide includes step-by-step multiplication of terms, combining like terms, and final simplification. Suitable for high school algebra students.

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