Question

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)

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. First, distribute \(-4x\) to each term in the second polynomial \((3x^2 - x - 1)\):

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

So, combining these yields:
\[
-12x^3 + 4x^2 + 4x
\]

2. Next, distribute \(-3\) to each term in the polynomial:

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

Combining these gives:
\[
-9x^2 + 3x + 3
\]

3. Now, we combine all these results together:

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

4. Combine like terms:

\[
-12x^3 + (4x^2 - 9x^2) + (4x + 3x) + 3
\]
\[
-12x^3 - 5x^2 + 7x + 3
\]

The expression \((-4x - 3)(3x^2 - x - 1)\) in standard form is:

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