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

Question

3883 views around the world

You can reuse this answer
Creative Commons License

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 $n=5$ .

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