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

To find the product of \((3q+4)(4q+2)\), we will use the distributive property (also known as the FOIL method for binomials). FOIL stands for First, Outer, Inner, Last, which are the terms we need to multiply together.<br /><br />1. **First**: Multiply the first terms in each binomial:<br /> \[<br /> 3q \cdot 4q = 12q^2<br /> \]<br /><br />2. **Outer**: Multiply the outer terms in the binomials:<br /> \[<br /> 3q \cdot 2 = 6q<br /> \]<br /><br />3. **Inner**: Multiply the inner terms in the binomials:<br /> \[<br /> 4 \cdot 4q = 16q<br /> \]<br /><br />4. **Last**: Multiply the last terms in each binomial:<br /> \[<br /> 4 \cdot 2 = 8<br /> \]<br /><br />Now, combine all these results:<br />\[<br />12q^2 + 6q + 16q + 8<br />\]<br /><br />Next, combine the like terms (\(6q\) and \(16q\)):<br />\[<br />12q^2 + 22q + 8<br />\]<br /><br />So, the simplified product of \((3q+4)(4q+2)\) is:<br />\[<br />\boxed{12q^2 + 22q + 8}<br />\]