Question 915742
Make trial binomial factors to logically test.

You want p for one part and q for the other part; but along with q, you need mostl likely a 2 and a 5.


Try starting this way:
(p____2q)(p_____5q)
You know operation signs will need to be chosen between each number in each binomial.  First think about the INNER and OUTER terms which would be summed.
{{{p^2}}}, {{{2pq}}}, {{{5pq}}}, {{{10q^2}}};
You know how the first term and the last term will fit.   Now check the terms of pq.  You need for their sum to be negative to fit  {{{-7pq}}}, which they do fit perfectly IF negative signs are placed between the numbers in each binomial:
{{{highlight((p-2q)(p-5q))}}}.
The LAST position term will be {{{10q^2}}} without any trouble.



The acronym for managing multiplication of two binomials to give the four starter terms is FOIL, standing for FIRST, OUTER, INNER, LAST.