Use the FOIL method to multiply the binomials. (x-6y)(3x+5y) (x-6y)(3x+5y)= square (Simplify your answer.)

To multiply the binomials \((x - 6y)(3x + 5y)\) using the FOIL method, we follow these steps:<br /><br />1. **First**: Multiply the first terms in each binomial:<br /> \[<br /> x \cdot 3x = 3x^2<br /> \]<br /><br />2. **Outer**: Multiply the outer terms in the product:<br /> \[<br /> x \cdot 5y = 5xy<br /> \]<br /><br />3. **Inner**: Multiply the inner terms:<br /> \[<br /> -6y \cdot 3x = -18xy<br /> \]<br /><br />4. **Last**: Multiply the last terms in each binomial:<br /> \[<br /> -6y \cdot 5y = -30y^2<br /> \]<br /><br />Now, combine all these results:<br />\[<br />3x^2 + 5xy - 18xy - 30y^2<br />\]<br /><br />Combine like terms (\(5xy\) and \(-18xy\)):<br />\[<br />3x^2 - 13xy - 30y^2<br />\]<br /><br />Thus, the simplified expression is:<br />\[<br />(x - 6y)(3x + 5y) = 3x^2 - 13xy - 30y^2<br />\]