Find the product. Simplify your answer. (4u+3)(2u+3) square

To find the product of \((4u+3)(2u+3)\), we will use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step process:<br /><br />1. **First**: Multiply the first terms in each binomial:<br /> \[<br /> 4u \cdot 2u = 8u^2<br /> \]<br /><br />2. **Outer**: Multiply the outer terms in the binomials:<br /> \[<br /> 4u \cdot 3 = 12u<br /> \]<br /><br />3. **Inner**: Multiply the inner terms in the binomials:<br /> \[<br /> 3 \cdot 2u = 6u<br /> \]<br /><br />4. **Last**: Multiply the last terms in each binomial:<br /> \[<br /> 3 \cdot 3 = 9<br /> \]<br /><br />Now, combine all these products:<br />\[<br />8u^2 + 12u + 6u + 9<br />\]<br /><br />Next, combine the like terms (\(12u\) and \(6u\)):<br />\[<br />8u^2 + 18u + 9<br />\]<br /><br />So, the simplified product of \((4u+3)(2u+3)\) is:<br />\[<br />\boxed{8u^2 + 18u + 9}<br />\]