Question

Multiply the polynomials

(4x^2+4x+6)(7x+5)

Answer 1

To multiply the polynomials \( (4x^2 + 4x + 6)(7x + 5) \), we will apply the distributive property (also known as the FOIL method in this case).

1. **Distribute \( 7x \) across each term in the first polynomial:**

\[
7x \cdot 4x^2 + 7x \cdot 4x + 7x \cdot 6
\]

This results in:

\[
28x^3 + 28x^2 + 42x
\]

2. **Now, distribute \( 5 \) across each term in the first polynomial:**

\[
5 \cdot 4x^2 + 5 \cdot 4x + 5 \cdot 6
\]

This results in:

\[
20x^2 + 20x + 30
\]

3. **Now, combine all the terms from both distributions:**

\[
28x^3 + 28x^2 + 42x + 20x^2 + 20x + 30
\]

4. **Combine like terms:**

- The \( x^2 \) terms: \( 28x^2 + 20x^2 = 48x^2 \)
- The \( x \) terms: \( 42x + 20x = 62x \)

Thus, the combined expression becomes:

\[
28x^3 + 48x^2 + 62x + 30
\]

Therefore, the final result of multiplying the polynomials \( (4x^2 + 4x + 6)(7x + 5) \) is:

\[
\boxed{28x^3 + 48x^2 + 62x + 30}
\]