Question

Factorise the following expressions.

(i) p2

+6p+8 (ii) q2

–10q+21​

Answer 1

Step-by-step explanation:

${p}^{2} + 6p + 8 \\ \\ = {p}^{2} + (4 + 2)p + 8 \\ \\ = {p}^{2} + 4p + 2p + 8 \\ \\ = p(p + 4) + 2(p + 4) \\ \\ = (p + 4)( p + 2) \\ \\ \\ \\ \\ {q}^{2} - 10q + 21 \\ \\ = {q}^{2} - (7 + 3)q + 21 \\ \\ = {q}^{2} - 7q - 3q + 21 \\ \\ = q(q - 7) - 3(q - 7) \\ \\ = (q - 7)( q - 3)$

Answer 2

Answer:

(i) p² + 6p + 8 = (p + 4)(p + 2)

(ii) q² - 10q + 21 = (q - 7)(q - 3)

Step-by-step explanation:

► To factorise p² + 6p + 8

• 6p can also be written as 2p + 4p

p² + 6p + 8  →  p² + 2p + 4p + 8

⇒ p(p + 2) + 4(p + 2)

⇒ (p + 4)(p + 2)

∴ p² + 6p + 8 = (p + 4)(p + 2)

► To factorise q² - 10q + 21

• -10p can also be written as -3p + -7p

q² - 10q + 21  →  q² - 3q - 7q + 21

⇒ q(q - 3) - 7(q - 3)

⇒ (q - 7)(q - 3)

∴ q² - 10q + 21 = (q - 7)(q - 3)