Question

Multiply the polynomials
(x + 3) (3^2 + 8x + 9)

Answer 1

To multiply the polynomials \((x + 3)(3^2 + 8x + 9)\), we'll first simplify the second polynomial.

Calculating \(3^2\):
\[
3^2 = 9
\]
Now, we can rewrite the second polynomial:
\[
3^2 + 8x + 9 = 9 + 8x + 9 = 8x + 18
\]

So, we need to multiply:
\[
(x + 3)(8x + 18)
\]

Now we can use the distributive property (also known as the FOIL method for binomials):

1. First, distribute \(x\):
\[
x \cdot 8x = 8x^2
\]
\[
x \cdot 18 = 18x
\]

2. Next, distribute \(3\):
\[
3 \cdot 8x = 24x
\]
\[
3 \cdot 18 = 54
\]

Now, combine all the terms:
\[
8x^2 + 18x + 24x + 54
\]

Combine like terms (\(18x + 24x\)):
\[
8x^2 + 42x + 54
\]

Thus, the result of multiplying the polynomials \((x + 3)(3^2 + 8x + 9)\) is:
\[
\boxed{8x^2 + 42x + 54}
\]