Question

Expand the expression to a polynomial in standard form:
left parenthesis, 3, x, plus, 8, right parenthesis, left parenthesis, 3, x, squared, plus, x, minus, 1, right parenthesis
(3x+8)(3x
2
+x−1)

Answer 1

To expand the expression \((3x + 8)(3x^2 + x - 1)\), we'll use the distributive property (also known as the FOIL method for binomials). We'll multiply each term in the first polynomial by each term in the second polynomial.

1. **Multiply \(3x\) by each term in \(3x^2 + x - 1\)**:
- \(3x \cdot 3x^2 = 9x^3\)
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-1) = -3x\)

So, this part gives us:
\[
9x^3 + 3x^2 - 3x
\]

2. **Multiply \(8\) by each term in \(3x^2 + x - 1\)**:
- \(8 \cdot 3x^2 = 24x^2\)
- \(8 \cdot x = 8x\)
- \(8 \cdot (-1) = -8\)

So, this part gives us:
\[
24x^2 + 8x - 8
\]

3. **Combine all the terms together**:
\[
9x^3 + 3x^2 - 3x + 24x^2 + 8x - 8
\]

4. **Combine like terms**:
- \(9x^3\)
- Combine \(3x^2 + 24x^2 = 27x^2\)
- Combine \(-3x + 8x = 5x\)
- The constant term is \(-8\)

So, the complete expanded expression is:
\[
\boxed{9x^3 + 27x^2 + 5x - 8}
\]