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An expression is shown below:

3x3y + 12xy − 9x2y − 36y
First Rewrite the expression so that the GCF is factored completely. Show the steps of your work.
Then Rewrite the expression completely factored. Show the steps of your work.

Respuesta :

josephinepitocco

Answer:

Part A: so the GCF is 3y, 

We need to rewrite the equation such as: 

-36 as -12 · 3, -9 as -3 · 3, 12 as 4 · 3

It will look like this: 

3x^3 y +4 · 3xy + 3 · 3x^2 y + 4 · 3 · 3y

We then need to factor out 3y:

3y(x^3 + 4x - 3x^2 - 12)

Part b: factor out completely

3y(x^3 + 4x - 3x^2 - 12)

So, we need to do the following:

3y{x^2(x-3) + 4 (x-3)}

we then get the final factor: 3y(x - 3) (x^2 + 4)

Step-by-step explanation:

The factored expression is:

[tex]3y(x^3 + 4x - 3x^2 - 12)[/tex]

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To factor the expression:

  • First, we need to find the greatest common factor of the numeric and symbolic coefficients.
  • Then, we divide each term of the expression by it's gcf.

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The expression is:

[tex]3x^3y + 12xy - 9x^2y - 36y[/tex]

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The numeric coefficients are: 3, 12, 9, 36

The gcf of the numeric coefficients is:

3 - 12 - 9 - 36|3

1 - 4 - 3 - 12

The gcf of the numeric coefficients is 3, as 3 is the only number by which 3, 12, 9 and 36 are all divisible.

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The symbolic coefficients are: [tex]x^3y, xy, x^2y, y[/tex]

The only common term is y, so y is the gcf of the symbolic coefficients.

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The gcf of the entire expression is the multiplication of the gcfs of the numeric and of the symbolic coefficients, so it is 3y.

Now, to factore the expression:

[tex]3x^3y + 12xy - 9x^2y - 36y = 3y(\frac{3x^3y}{3y} + \frac{12xy}{3y} - \frac{9x^2y}{3y} - \frac{36y}{3y}) = 3y(x^3 + 4x - 3x^2 - 12)[/tex]

The factored expression is:

[tex]3y(x^3 + 4x - 3x^2 - 12)[/tex]

A similar problem is given at https://brainly.com/question/20691631

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