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mash [69]
3 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]3 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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*PLS HELP
n200080 [17]

Answer:

  y = 3x +4

Step-by-step explanation:

The equation for the parallel line will have the same x- and y-coefficients, but a different constant. You can put the given point values into the equation to see what the constant needs to be:

  y = 3x + b

  10 = 3·2 + b . . . . . . substitute x=2, y=10

  4 = b . . . . . . . . . . . . subtract 6

The equation of the line is ...

  y = 3x +4

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2 years ago
Simplify 5 cube root of 72
goldenfox [79]
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4 0
3 years ago
Simplify the expression below, I really just need the steps I have the answer (also can someone tell me how to edit points on th
Sloan [31]

Answer:  3x^2y\sqrt[3]{y}\\\\

Work Shown:

\sqrt[3]{27x^{6}y^{4}}\\\\\sqrt[3]{3^3x^{3+3}y^{3+1}}\\\\\sqrt[3]{3^3x^{3}*x^{3}*y^{3}*y^{1}}\\\\\sqrt[3]{3^3x^{2*3}*y^{3}*y}\\\\\sqrt[3]{\left(3x^2y\right)^3*y}\\\\\sqrt[3]{\left(3x^2y\right)^3}*\sqrt[3]{y}\\\\3x^2y\sqrt[3]{y}\\\\

Explanation:

As the steps above show, the goal is to factor the expression under the root in terms of pulling out cubed terms. That way when we apply the cube root to them, the exponents cancel. We cannot factor the y term completely, so we have a bit of leftovers.

4 0
3 years ago
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zepelin [54]
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6 0
2 years ago
Read 2 more answers
Let sin A= -3/5 with 270°&lt; A&lt; 360°. Find the following.<br> sin A/2
GREYUIT [131]

Answer:

1/sqrt10

Step-by-step explanation:

1) Find out cosA using formula (cosA)^2+(sinA)^2=1

The module of cosA= sqrt (1- (-3/5)^2)= sqrt 16/25=4/5

So cosA=-4/5 or cosA=4/5.

Due to the condition 270degrees< A<360 degrees, 0<cosA<1 that's why cosA=4/5.

2) Find sinA/2 using a formula cosA= 1-2sinA/2*sinA/2 where cosA=4/5.

(sinA/2)^2= 0.1

sinA= sqrt 0.1= 1/ sqrt10 or sinA= - sqrt 0.1= -1/sqrt10

But 270°< A< 360°, then 270/2°<A/2<360/2°

135°<A/2<180°, so sinA/2 must be positive and the only correct answer is

sin A/2= 1/sqrt10

6 0
3 years ago
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