How do you factor #p^2-14p+49# using the perfect squares formula?

2 Answers
Apr 15, 2017

Answer:

#(p-7)(p-7)#

Explanation:

49 is #7^2# so we need to make -14p and +49; therefore both signs in the brackets must minus.

#(p-7)(p-7)#

Tip; The perfect square formula can be a bit confusing. Just use your intuition if you know the answer. That is what I do and I do not get penalised for it. Just use the formula if necessary.

Apr 15, 2017

Answer:

See below.

Explanation:

The perfect squares formula is in the form: #(x-a)^2#. Expanding,

#(x-a)^2=x^2-2ax+a^2#

Set this equal to #x^2-14x+49#.

So:

#a^2=49#, or #a=\pm7#

But,

#-2ax=-14x#, so #a=7#.

Thus, #p^2-14p+49=(p-7)^2#.

Or, factor by splitting.

#p^2-7p-7p+49#

#p(p-7)-7(p-7)#

#(p-7)(p-7)#

#=(p-7)^2#