Question

which expression is equivalent to the product of (2h^2 + 9h - 5) and (3h + 6)

Answer 1

To find the expression that is equivalent to the product of \((2h^2 + 9h - 5)\) and \((3h + 6)\), we will use the distributive property (also known as the FOIL method for binomials) to expand the product.

The expression can be written as:

\[
(2h^2 + 9h - 5)(3h + 6)
\]

We will distribute each term in the first polynomial to each term in the second polynomial.

1. **Distributing \(2h^2\)**:
- \(2h^2 \cdot 3h = 6h^3\)
- \(2h^2 \cdot 6 = 12h^2\)

2. **Distributing \(9h\)**:
- \(9h \cdot 3h = 27h^2\)
- \(9h \cdot 6 = 54h\)

3. **Distributing \(-5\)**:
- \(-5 \cdot 3h = -15h\)
- \(-5 \cdot 6 = -30\)

Now, we will combine all the terms we obtained:

\[
6h^3 + 12h^2 + 27h^2 + 54h - 15h - 30
\]

Next, we gather like terms:

- \(6h^3\)
- For the \(h^2\) terms: \(12h^2 + 27h^2 = 39h^2\)
- For the \(h\) terms: \(54h - 15h = 39h\)

So the final expression becomes:

\[
6h^3 + 39h^2 + 39h - 30
\]

Thus, the expression equivalent to the product of \((2h^2 + 9h - 5)\) and \((3h + 6)\) is:

\[
\boxed{6h^3 + 39h^2 + 39h - 30}
\]