By using the contrapositive implication, prove that, IF
$$ a^2(b^2 -2b)$$ is odd then, a and b are odd where a, b ∈ ℤ
Suppose a odd and b is even
Show that $$a^2 (b^2 – 2b) = 2k$$ $$(2k + 1)^2 [(2k)^2 – 2(2k)]$$ $$(4k^2 + 4k + 1) (4k^2 – 4k)$$ $$(4k^2 + 4k + 1)[(2)(2k^2) – 2k)]$$
Therefore it fits the form where 2k $$(2(2k^2 – 2k))$$ ∈ ℤ
Thus $$a^2 (b^2 – 2b)$$ is even