Question

expand and simplify (x+3)(x-3)(3x+2)

Answer 1

To expand and simplify the expression \((x + 3)(x - 3)(3x + 2)\), we can follow these steps:

1. **Recognize the difference of squares**: The expression \((x + 3)(x - 3)\) can be simplified first because it represents a difference of squares.

\[
(x + 3)(x - 3) = x^2 - 9
\]

2. **Substitute the result into the third factor**: Now we replace \((x + 3)(x - 3)\) with \(x^2 - 9\):

\[
(x^2 - 9)(3x + 2)
\]

3. **Distribute \((3x + 2)\) over \((x^2 - 9)\)**:

\[
(x^2 - 9)(3x + 2) = x^2(3x + 2) - 9(3x + 2)
\]

Now, distributing each term:

\[
x^2(3x + 2) = 3x^3 + 2x^2
\]

\[
-9(3x + 2) = -27x - 18
\]

4. **Combine all the terms**:

\[
3x^3 + 2x^2 - 27x - 18
\]

Now, the expanded and simplified form of \((x + 3)(x - 3)(3x + 2)\) is:

\[
\boxed{3x^3 + 2x^2 - 27x - 18}
\]