Factor out completly: 6x^2y − 3xy − 24xy^2 + 12y^2

The factor of 6x²y − 3xy − 24xy² + 12y² is 3y(2x - 1)(x - 4y)

Given:

6x²y − 3xy − 24xy² + 12y²

find the highest common factor of all the coefficient of each term

6 = 1, 2, 3, 6

6 = 1, 2, 3, 63 = 1, 3

6 = 1, 2, 3, 63 = 1, 324 = 1, 2, 3, 4, 6, 8, 12, 24

6 = 1, 2, 3, 63 = 1, 324 = 1, 2, 3, 4, 6, 8, 12, 2412 = 1, 2, 3, 4, 6, 8, 12

The highest common factor of all the coefficient of each term is 3

So,

6x²y − 3xy − 24xy² + 12y²

= 3y(2x² - x - 8xy + 4y)

(2x² - x - 8xy + 4y) = (2x - 1)(x - 4y)

Therefore,

6x²y − 3xy − 24xy² + 12y = 3y(2x - 1)(x - 4y)

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x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

93-8=85

855=17

17*4=68

there are 68 purple marbles in that bag