Expand the expression to a polynomial in standard form:

Question

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: \[ \boxed{-6x^3 - 15x^2 - 14x - 4} \]