Question

Expand the expression to a polynomial in standard form:
(3x+2)(3x^2 −3x−7)

Answer 1

To expand the expression \((3x + 2)(3x^2 - 3x - 7)\), you can use the distributive property (also known as the FOIL method for binomials).

Here’s how to do it step by step:

1. Distribute \(3x\) to each term in the second polynomial:
\[
3x \cdot 3x^2 = 9x^3
\]
\[
3x \cdot (-3x) = -9x^2
\]
\[
3x \cdot (-7) = -21x
\]

2. Now distribute \(2\) to each term in the second polynomial:
\[
2 \cdot 3x^2 = 6x^2
\]
\[
2 \cdot (-3x) = -6x
\]
\[
2 \cdot (-7) = -14
\]

3. Combine all these results together:
\[
9x^3 - 9x^2 - 21x + 6x^2 - 6x - 14
\]

4. Now, combine like terms:
- For \(x^2\) terms: \(-9x^2 + 6x^2 = -3x^2\)
- For \(x\) terms: \(-21x - 6x = -27x\)

So, the expression simplifies to:
\[
9x^3 - 3x^2 - 27x - 14
\]

Thus, the final answer in polynomial standard form is:
\[
\boxed{9x^3 - 3x^2 - 27x - 14}
\]