expand the expression to a polynomial in standard form

Question

(-4x-3)(3x^2-x-1) use symbols so dont say boxed

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 will distribute each term in the first polynomial to each term in the second polynomial.

1. Distributing \(-4x\):

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

2. Distributing \(-3\):

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

Now, we will combine these results:

\[ -12x^3 + (4x^2 - 9x^2) + (4x + 3x) + 3 \]

This simplifies to:

\[ -12x^3 - 5x^2 + 7x + 3 \]

Thus, the polynomial in standard form is:

\(-12x^3 - 5x^2 + 7x + 3\)