How do you factor #a^2+20a+64#?

1 Answer
George C.
Jun 8, 2015

#a^2+20a+64 = (a+4)(a+16)#

Explanation:

#(a+m)(a+n) = a^2+(m+n)a+(mxxn)#

So if we can find #m# and #n# with #m+n = 20# and #mxxn = 64# then we have our factorisation.

#64 = 2^6# factors into the following pairs:

#1 xx 64#, #2 xx 32#, #4 xx 16#, #8 xx 8#

It's easy to spot that the pair #4, 16# will work.

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