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If P(k) = k2 (k + 3) (k2 – 1) is true, then what is P(k + 1)?

If P(k) = k2 (k + 3) (k2 – 1) is true, then what is P(k + 1)? Correct Answer (k + 1)2 (k + 4) k (k + 2)

In mathematical induction, if P(k) is true, we need to prove that P(k + 1) is also true. Here P(k + 1) is found by substituting (k + 1) in place of k. P(k + 1) = (k + 1)2 (k + 1 + 3) ((k + 1)2 – 1) P(k + 1) = (k + 1)2 (k + 4) (k2 + 1 + 2k – 1) P(k + 1) = (k + 1)2 (k + 4) (k2 + 2k) P(k + 1) = (k + 1)2 (k + 4) k (k +2)

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