Question

expand the expression to a polynomial in standard form

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