Find the product of (1.5*w* + 4)(*w* + 4).

To find the product of \((1.5w + 4)(w + 4)\), we will use the distributive property (also known as the FOIL method for binomials). The distributive property states that:

\[
(a + b)(c + d) = ac + ad + bc + bd
\]

Here, \(a = 1.5w\), \(b = 4\), \(c = w\), and \(d = 4\). Now let's multiply each term:

\[
(1.5w)(w) + (1.5w)(4) + (4)(w) + (4)(4)
\]

\[
= 1.5w^2 + 6w + 4w + 16
\]

Combine like terms:

\[
1.5w^2 + 10w + 16
\]

So, the product of \((1.5w + 4)(w + 4)\) is:

\[
\boxed{1.5w^2 + 10w + 16}
\]

Would you like further details or have any questions?

### Related Questions:
1. How would the product change if the coefficients of \(w\) were different?
2. What if the expression inside the parentheses included a constant term?
3. How would you factor the expression \(1.5w^2 + 10w + 16\)?
4. Can you find the roots of the equation \(1.5w^2 + 10w + 16 = 0\)?
5. How does the distributive property apply to polynomials with more than two terms?

### Tip:
When multiplying binomials, always remember to distribute each term in the first binomial to every term in the second binomial to ensure all combinations are covered.

Learn how to multiply (1.5w + 4)(w + 4) using the distributive property step-by-step. This problem involves algebraic manipulation and the distributive property of polynomials. Suitable for high school students.

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