Question

find the product of the polynomials
(-p+q)(-1-q)

Answer 1

To find the product of the polynomials \((-p + q)(-1 - q)\), we can use the distributive property (also known as the FOIL method for binomials). We will multiply each term in the first polynomial by each term in the second polynomial.

Let's calculate it step by step:

1. Distribute \(-p\) to both terms in the second polynomial:
\[
-p \cdot (-1) = p
\]
\[
-p \cdot (-q) = pq
\]

2. Distribute \(q\) to both terms in the second polynomial:
\[
q \cdot (-1) = -q
\]
\[
q \cdot (-q) = -q^2
\]

Now, combine all these results:
\[
p + pq - q - q^2
\]

Rearranging terms, we get:
\[
pq - q^2 + p - q
\]

Thus, the final result for the product of the polynomials \((-p + q)(-1 - q)\) is:
\[
pq - q^2 + p - q
\]