How do you factor #a^2b^2 - 7ab + 10#?

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Answer 1 · 2015-05-17T20:19:12

Notice that #7 = 2 + 5# and #10 = 2 xx 5#.

So we can factor:

#a^2b^2-7ab+10 = (ab)^2-7(ab)+10#

#= (ab-2)(ab-5)#

This is an instance of the identity:

#(x-m)(x-n) = x^2-(m+n)x+(mxxn)#

with #x = ab#, #m=2# and #n=5#.