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Expand the expression to a polynomial in standard form:

left parenthesis, minus, 4, x, minus, 3, right parenthesis, left parenthesis, 3, x, squared, minus, x, minus, 1, right parenthesis

(−4x−3)(3x
2
−x−1)

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

1 answer

To expand the expression \((-4x - 3)(3x^2 - x - 1)\) and write it in standard form, we will use the distributive property (also known as the FOIL method for binomials):

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

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

  3. Now, combine all these results: \[ -12x^3 + 4x^2 + 4x - 9x^2 + 3x + 3 \]

  4. Combine like terms:

    • The \(x^2\) terms: \(4x^2 - 9x^2 = -5x^2\)
    • The \(x\) terms: \(4x + 3x = 7x\)

  5. Therefore, the expression simplifies to: \[ -12x^3 - 5x^2 + 7x + 3 \]

Putting it all together, we have:

\[ \text{Final answer: } -12x^3 - 5x^2 + 7x + 3 \]