Question 84174
Do you mean to "expand" or "multiply"?  If you have a product of two binomials, usually you are asked to multiply the product.  This would be what we sometimes call "F OI L".  In this case:
(p-3)(p+5)


FIRST times FIRST = {{{p*p = p^2}}}
OUTER times OUTER = {{{5*p = 5p }}}
INNER times INNER = {{{-3*p = -3p }}}
LAST times LAST = {{{-3*5= -15}}}


Add these terms together and combine like terms:
{{{p^2 + 5p -3p -15 }}}
{{{p^2 +2p-15}}}


Now, if you were given this trinomial, you would be asked to "factor it", which is to change this trinomial to a product of two binomials that you started out with.


For more help with this topic, see my Lesson Plans in algebra.com, or my website under "Basic Algebra", "Samples from Basic Algebra: One Step at a Time", "Chapter 2", "Section 2.01."


R^2 at SCC