How do you factor #a^ { 2} + 9a f + 20f ^ { 2}#?

1 Answer
Nam D.
Jan 26, 2018

#(a+4f)(a+5f)#

Explanation:

#a^2+9af+20f^2#

We we have to "split" the middle term into two numbers, let's say #x# and #y#, so that their sum #(x+y)# equals to #9#, and their product #x*y# equals to #20#. This is the most tricky part.

I find that #4+5=9#, and #4*5=20#, so our middle terms will be split into #4af# and #5af#.

#:. a^2+4af+5af+20f^2#

Factoring out,

#a(a+4f)+5f(a+4f)#

Now, factor out the common term to get the final answer.

#(a+4f)(a+5f)#

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