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Factorise the following expressions.

(i)

(ii)

(iii)

(i) P^{2} + 6p + 8

Here middle term 6p can be written as 4p + 2p

P^{2} + 6p + 8 = p^{2} + 4p + 2p + 8

Taking p common in first two terms and 2 common in last two terms

P^{2} + 6p + 8 = p^{2} + 4p + 2p + 8 = p(p + 4) + 2(p + 4) = (p + 4)(p + 2)

(ii) q^{2} - 10q + 21

Here middle term -10q can be written as 7q + 3q

q^{2} - 10q + 21 = q^{2} + 7q + 3q + 21

Taking q common in first two terms and 3 common in last two terms

q^{2} - 10q + 21 = q^{2} - 7q - 3q + 21 = q(q - 7) - 3(q - 7) = (q - 3)(q - 7)

(iii) P^{2} + 6p - 16

Here middle term 6p can be written as 8p - 2p

P^{2} + 6p - 16 = p^{2} + 8p - 2p - 16

Taking p common in first two terms and 2 common in last two terms

P^{2} + 6p + 8 = p^{2} + 8p - 2p - 16 = p(p + 8) - 2(p + 8) = (p + 8)(p - 2)

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