expand the expression to a polynomial in standard form

Question

(-4x-3)(3x^2-x-1)

you made me get the other question wrong so dont make me fail

Answer 1

To expand the expression \((-4x - 3)(3x^2 - x - 1)\), we'll use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(-4x\) to each term in the second polynomial:

   • \(-4x \cdot 3x^2 = -12x^3\)
   • \(-4x \cdot (-x) = 4x^2\)
   • \(-4x \cdot (-1) = 4x\)

2. Now distribute \(-3\) to each term in the second polynomial:

   • \(-3 \cdot 3x^2 = -9x^2\)
   • \(-3 \cdot (-x) = 3x\)
   • \(-3 \cdot (-1) = 3\)

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

3. Combine like terms:

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

After combining like terms, the expression becomes: \[ -12x^3 - 5x^2 + 7x + 3 \]

Thus, the polynomial in standard form is: \[ \boxed{-12x^3 - 5x^2 + 7x + 3} \]