How do you factor #7q^2 - 5pq - 7q + 5p# by grouping?

Question

855 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-29T23:27:50

#(q-1)(7q-5p)#

Treat the term as two different groups of two.

#=(7q^2-5pq)-(7q-5p)#

Note that the sign on #5p# changes to #-5p# since a negative has been factored from the last two terms.

Now, take a common term from each of these pairs.

The factor #q# is common in #7q^2-5pq#. There is no common factor in #7q-5p# other than #1#, which may seem cheap, but is necessary.

#=q(7q-5p)-1(7q-5p)#

Notice that now the #(7q-5p)# term is common to both the #q# and #-1#. Thus the expression can be factored as:

#=(q-1)(7q-5p)#