Question

Multiply the two polynomials below, showing all work.

(x^2−1)(−2x+5)

Answer 1

To multiply the two polynomials \((x^2 - 1)(-2x + 5)\), we will use the distributive property (also known as the FOIL method for two binomials).

1. Distribute each term in the first polynomial \(x^2 - 1\) to each term in the second polynomial \(-2x + 5\):

\[
(x^2 - 1)(-2x + 5) = x^2(-2x) + x^2(5) - 1(-2x) - 1(5)
\]

2. Perform the multiplication for each term:

- For \(x^2(-2x)\):
\[
x^2 \cdot -2x = -2x^3
\]

- For \(x^2(5)\):
\[
x^2 \cdot 5 = 5x^2
\]

- For \(-1(-2x)\):
\[
-1 \cdot -2x = 2x
\]

- For \(-1(5)\):
\[
-1 \cdot 5 = -5
\]

3. Combine all these results together:
\[
-2x^3 + 5x^2 + 2x - 5
\]

4. The final result of multiplying the polynomials is:
\[
\boxed{-2x^3 + 5x^2 + 2x - 5}
\]