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Nataliya [291]
3 years ago
11

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

Mathematics
2 answers:
charle [14.2K]3 years ago
7 0

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)

maxonik [38]3 years ago
5 0

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.

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