How do you evaluate #(\sqrt { p } - a ) ( \sqrt { p } + a )#?

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Answer 1 · 2018-04-04T03:33:58

#p - a^2#

#(sqrtp-a)(sqrtp+a)#

Let's write out what each of them multiplies to in order to make it clearer:

#sqrtp * sqrtp = p#

#sqrtp * a = asqrtp#

#-a * sqrtp = -asqrtp#

#-a * a = -a^2#

When we combine them all together we get:
#p + asqrtp - asqrtp - a^2#

We can still simplify this as #asqrtp and -asqrtp# are in common. So the final answer is:
#p - a^2#

Hope this helps!