Question

(7x^2+9x+7)(9x-4)

multiply the polynomials

Answer 1

To multiply the polynomials \( (7x^2 + 9x + 7)(9x - 4) \), we'll use the distributive property (also known as the FOIL method for binomials).

We can distribute each term from the first polynomial to each term in the second polynomial:

1. Multiply \( 7x^2 \) by each term in \( (9x - 4) \):
- \( 7x^2 \cdot 9x = 63x^3 \)
- \( 7x^2 \cdot (-4) = -28x^2 \)

2. Multiply \( 9x \) by each term in \( (9x - 4) \):
- \( 9x \cdot 9x = 81x^2 \)
- \( 9x \cdot (-4) = -36x \)

3. Multiply \( 7 \) by each term in \( (9x - 4) \):
- \( 7 \cdot 9x = 63x \)
- \( 7 \cdot (-4) = -28 \)

Now, combine all these results together:
\[
63x^3 + (-28x^2 + 81x^2) + (-36x + 63x) - 28
\]

Combine like terms:
- For \( x^2 \) terms: \( -28x^2 + 81x^2 = 53x^2 \)
- For \( x \) terms: \( -36x + 63x = 27x \)

Thus, the final result is:
\[
63x^3 + 53x^2 + 27x - 28
\]

So, the product of the polynomials \( (7x^2 + 9x + 7)(9x - 4) \) is:
\[
\boxed{63x^3 + 53x^2 + 27x - 28}
\]