Point N is taken in triangle ABC on side BC, BN = 4NC Express vector AN through vectors a = BA and b = BC.

According to the condition of the problem, we can compose the following formula to express vectors:
AN = a + b + 1/8 * b
We continue to express vectors:
(AN = NC + AC) * (AC = AB + BC);
Let’s transform and get the answer:
(AN = NC + AB + BC) * (BC = 8NC).
Answer: (AN = NC + AB + BC) * (BC = 8NC).



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