Question

expand the expression to a polynomial in standard form

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


you made me get the other questionswrong so dont make me fail

Answer 1

To expand the expression \((-4x - 3)(3x^2 - x - 1)\), we will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by 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, combine all the resulting products:

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

Next, combine like terms:

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

Putting it all together, we have:

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

Thus, the polynomial in standard form is:

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