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Factorisation by Regrouping Terms

pq2+qp-1-1=? ...

Question

$p q^{2} + q (p - 1) - 1 = ? (a) (p q + 1) (q - 1) (b) p (q + 1) (p - 1) (c) q (p - 1) (q + 1) (d) (p q - 1) (q + 1)$

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Solution

$p q^{2} + q (p - 1) - 1 = p q^{2} + p q - q - 1 = p q (q + 1) - 1 (q + 1) = (q + 1) (p q - 1) = (p q - 1) (q + 1)$

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