Step-by-step explanation:
[tex]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.[/tex]
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)
