What is the first step in factoring the following problem?
(5a^2 - 11a + 10)^2 - (4a^2 -15a + 6)^2
No.
$(5a^2 - 11a + 10) - (4a^2 - 15a + 6) = $
$5a^2 - 11a + 10 - 4a^2 + 15a - 6 = $
$5a^2 - 4a^2 - 11a + 15a + 10 - 6 = $
$a^2 + 4a + 4$
and
$(5a^2 - 11a + 10) + (4a^2 - 15a + 6) = $
$5a^2 - 11a + 10 + 4a^2 - 15a + 6 = $
$5a^2 + 4a^2 - 11a - 15a + 10 + 6 = $
$9a^2 - 26a + 16$
Substitute them back in:
$(a^2 + 4a + 4)(9a^2 - 26a + 16) = $
Do not multiply them back together. Try to factor each trinomial further into a pair of binomial factors.