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

Question

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

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Sarah 2 weeks 2021-10-03T19:30:01+00:00 2 Answers 0

Answers ( )

    0
    2021-10-03T19:31:05+00:00

    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)

    0
    2021-10-03T19:31:56+00:00

    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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45:7+7-4:2-5:5*4+35:2 =? ( )