Question

Ch = Algebraic Expression 1. Resolve into factors:

a) (p - r)(pr + r)
b) (pr - r)(p + r)
c) (pq - r)(r^2 + 1)
d) (r - p)(p^2 + q^2)

Answer 1

The given algebraic expressions are resolved into factors, with (b) having a factor of r that can be factored out. Expressions (a), (c), and (d) are already fully factored and do not require further simplification.

Step-by-step explanation:

The question asks to resolve into factors the given algebraic expressions. Let's consider each expression one by one:

• a) (p - r)(pr + r): Since there are no common terms to eliminate between the two factors, this expression is already fully factored.
• b) (pr - r)(p + r): Here, we can factor out an r from the first factor to get r(p - 1)(p + r).
• c) (pq - r)(r^2 + 1): This expression is also fully factored, as there are no common terms that can be factored out or simplified.
• d) (r - p)(p^2 + q^2): This expression is similarly already factored, with no common terms to simplify between the factors.

To verify these are indeed the factors, you can foiler multiply them out and check if you get back the original expressions, ensuring that the algebra is reasonable.