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

To find the product of \((4j+3)(j+4)\), 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 /> \[<br /> 4j \cdot j = 4j^2<br /> \]<br /><br />2. **Outer**: Multiply the outer terms in the binomials:<br /> \[<br /> 4j \cdot 4 = 16j<br /> \]<br /><br />3. **Inner**: Multiply the inner terms in the binomials:<br /> \[<br /> 3 \cdot j = 3j<br /> \]<br /><br />4. **Last**: Multiply the last terms in each binomial:<br /> \[<br /> 3 \cdot 4 = 12<br /> \]<br /><br />Now, combine all these products:<br />\[<br />4j^2 + 16j + 3j + 12<br />\]<br /><br />Next, combine the like terms (\(16j\) and \(3j\)):<br />\[<br />4j^2 + 19j + 12<br />\]<br /><br />So, the simplified product of \((4j+3)(j+4)\) is:<br />\[<br />\boxed{4j^2 + 19j + 12}<br />\]