Question

Expand the expression to a polynomial in standard form:
left parenthesis, 2, x, plus, 1, right parenthesis, left parenthesis, minus, 3, x, squared, minus, 6, x, minus, 4, right parenthesis

(2x+1)(−3x
2
−6x−4)

Solve the problem just like the example below
⬇️
Expand the expression to a polynomial in standard form:
left parenthesis, 4, x, minus, 3, right parenthesis, left parenthesis, 2, x, squared, minus, 2, x, minus, 5, right parenthesis

(4x−3)(2x
2
−2x−5)


Combine like terms:
8x³- 14x²-14x+15

Answer 1

To expand the expression \((2x + 1)(-3x^2 - 6x - 4)\) and write it as a polynomial in standard form, follow these steps:

1. **Distribute \(2x\) to each term in the second polynomial**:
\[
2x \cdot (-3x^2) = -6x^3
\]
\[
2x \cdot (-6x) = -12x^2
\]
\[
2x \cdot (-4) = -8x
\]

2. **Distribute \(1\) to each term in the second polynomial**:
\[
1 \cdot (-3x^2) = -3x^2
\]
\[
1 \cdot (-6x) = -6x
\]
\[
1 \cdot (-4) = -4
\]

3. **Combine all the results**:
\[
-6x^3 + (-12x^2) + (-8x) + (-3x^2) + (-6x) + (-4)
\]

4. **Combine like terms**:
- The \(x^3\) term: \(-6x^3\)
- The \(x^2\) terms: \(-12x^2 - 3x^2 = -15x^2\)
- The \(x\) terms: \(-8x - 6x = -14x\)
- The constant term: \(-4\)

5. **Write the final polynomial in standard form**:
\[
-6x^3 - 15x^2 - 14x - 4
\]

So, the expanded expression in standard form is:
\[
\boxed{-6x^3 - 15x^2 - 14x - 4}
\]