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# 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 $$8 \times 2 = 16$$

$$p^2 + 6p – 16$$

$$= p^2 + 8p – 2p – 16$$

$$= p(p + 8) – 2(p + 8)$$

$$= (p + 8) (p – 2)$$