5. Factorise the following expressions.

(i) \(p^2 + 6p + 8\)

(ii) \(q^2 – 10q + 21\)

(iii) \(p^2 + 6p – 16\)

(i)Given:\( p^2 + 6p + 8\)

Here, 2 + 4 = 6 and \(2 \times 4 = 8\)

\(p^2 + 6p + 8\)

\(= p^2 + 2p + 4p + 8\)

\(= p (p + 2) + 4(p + 2)\)

\(= (p + 2) (p + 4)\)

(ii)Given: \(q^2 – 10q + 21\)

Here, 3 + 7 = 10 and \(3 \times 7 = 21\)

\(q^2 – 10q + 21\)

\(= q^2 – 3q – 7q + 21\)

\(= q(q – 3) – 7(q – 3)\)

\(= (q – 3) (q – 7)\)

(iii) Given:\(p^2 + 6p – 16\)

Here, 8 – 2 = 6 and \(8 \times 2 = 16\)

\(p^2 + 6p – 16\)

\(= p^2 + 8p – 2p – 16\)

\(= p(p + 8) – 2(p + 8)\)

\(= (p + 8) (p – 2)\)