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mash [69]
2 years ago
8

(08.01, 8.02 MC) An expression is shown below: 18x3y − 9x2y − 72xy3 + 36y3 Part A: Rewrite the expression so the GCF is factored

out of the polynomial. (3 points) Part B: Rewrite the expression completely factored. Show the steps of your work. (7 points) (10 points)
Mathematics
1 answer:
vitfil [10]2 years ago
7 0

Answer:

9y(2x - 1)(x - 2y)(x + 2y)

Step-by-step explanation:

Given

18x³y - 9x²y - 72xy³ + 36y³ ← factor out 9y from each term

= 9y(2x³ - x² - 8xy² + 4y²)

Factor the first/second and third/fourth term in the parenthesis

= 9y( x²(2x - 1) - 4y²(2x - 1)) ← factor out (2x - 1) from each term

= 9y(2x - 1)(x² - 4y²)

x² - 4y² is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4y²

= x² - (2y)² = (x - 2y)(x + 2y), hence

18x³y - 9x²y + 72xy³ + 36y³

= 9y(2x - 1)(x - 2y)(x + 2y) ← in factored form

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Answer:

The correct answer is B. -3.

Step-by-step explanation:

To solve this problem, we need to plug in -3 for all of the values of x in the equation.  If we do this, we get:

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Now, we can just simplify the expression found on the right side of the equation using PEMDAS.  First, we should perform the multiplication.

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Next, we should add our final two terms together.

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Therefore, the correct answer is -3.

Hope this helps!

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Answer:

See attachment.

Step-by-step explanation:

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The correct choice is shown in the attachment

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