Question

Factor completely: 30a^3–18a^2b–72b+120a

Answer 1

30a³ - 18a²b - 72b + 120a

5 · 6a³ + 3 · 6a²b + 12 · 6b + 20 · 6a

6(5a² - 3a²b - 12b + 20a)

5a² - 3a²b + 20a - 12b

(5a² - 3a²b) + (20a - 12b)

a²(5a - 3b) + 4(5a - 3b)

(5a - 3b) (a² + 4)

6(5a - 3b)(a² + 4)

Answer 2

Step-by-step explanation:

$30 {a}^{3} - 18 {a}^{2}b - 72b + 120a \\ = 30 {a}^{3} + 120a - 18 {a}^{2}b - 72b \\ = 30a( {a}^{2} + 4) - 18b( {a}^{2} + 4) \\ = ( {a}^{2} + 4) (30a - 18b) \\ = ( {a}^{2} + 4) \times 6(5a - 3b) \\ \purple{ \boxed{= 6(5a - 3b) ( {a}^{2} + 4)}}\\ are \: the \: required \: factors \: of \: given \: \\ expression.$