Question

completely factor the expression by grouping, if possible.
\\p^2 - pw - 7p + 7w\\

answer
how to enter your answer (opens in new window)
selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used.

( ) not factorable by grouping

Explanation:

Group the terms of the expression

We begin with the given four-term polynomial expression:

$$ p^2 - pw - 7p + 7w $$

We group the first two terms together and the last two terms together:

$$ (p^2 - pw) + (-7p + 7w) $$

Factor out the GCF from each group

For the first group, \(p^2 - pw\), the greatest common factor is \(p\):

$$ p^2 - pw = p(p - w) $$

For the second group, \(-7p + 7w\), we factor out \(-7\) to match the binomial factor:

$$ -7p + 7w = -7(p - w) $$

Substituting these back into our grouped expression gives:

$$ p(p - w) - 7(p - w) $$

Factor out the common binomial

Both terms now share a common binomial factor of \((p - w)\). We factor this out:

$$ (p - w)(p - 7) $$

This is the completely factored form of the expression.

Answer:

\((p - w)(p - 7)\)