Write out proof in paragraph form. include contradictions if necessary
5. prove that n(n+1) (2n+1) is always divisible by 6

If , then

which is of course divisible by 6.

Assume the claim holds for . Then if , we have

(I use the distributive property of multiplication to extract the first term, which we've assumed is divisible by 6)

The claim holds for if

is also divisible by 6. With some manipulation we can express this as

which is clearly divisible by 6, so the claim is true for , and this completes the proof (by induction).

-14

step-by-step explanation:

2x2 – 2(x+4)

=2x2-2（5+4）

=4-2×9

=4-18

=-14