Use the Binomial Theorem to expand (x - 2y)^3

Answers

Answer 1

Answer:
From Binomial Theorem (x-2y)³:
( $((3)/(0)) x^(3)+( (3)/(1) ) x^(2) *(-2y)+( (3)/(2))x*( -2y)^(2) +( (3)/(3)) x^(0) (-2y)^(3) =$ $(3!)/(0!3!) x^(3)- (3!)/(1!2!) x^(2) 2y- (3!)/(2!1!)x4 y^(2)- (3!)/(3!0!)8 y^(3)$ =x³-6x²y-12xy²-8y³

Answer 2

Answer: $(x-2y)^3=x^3-6x^2y+12xy^2-8y^3$

Related Questions

All of the following fractions are equivalent to 1/2 , except:A.2/4 B.5/10 C.4/7 D.3/6
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how many rectangular prism can you make out of 20 snap of cubes
G(x)= 8x+2 g(?) = -62
The time that a traffic light remains yellow is 1 second more than 0.05 times the speed limit. 1. Write an equation that represents Y, the length of the time the light is yellow at x miles per hour.

A jar contains 24 coins: 10 quarters, 6 dimes, 2 nickels, and 6 pennies.What is the probability of randomly drawing _____ ?
1. a penny
2. a quarter
3. a coin that is not a penny

Answers

The probability of randomly drawing a penny is 6/24 or 1/4, since there are 6 pennies out of a total of 24 coins.

How to solve and What is Probability?

The probability of randomly drawing a quarter is 10/24 or 5/12, since there are 10 quarters out of a total of 24 coins. The probability of randomly drawing a coin that is not a penny is 18/24 or 3/4, since there are 18 coins that are not pennies out of a total of 24 coins.

Probability is the branch of mathematics that deals with measuring the likelihood or chance of an event or outcome occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability theory is used to make predictions and informed decisions based on available data in various fields, including statistics, finance, engineering, and science.

It involves understanding and analyzing random events, and determining the likelihood of specific outcomes. Probability is an essential tool for decision-making in various applications, such as risk analysis, game theory, and quality control.

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For which data sets is the median a better measure of center than the mean? Choose all answers that are correct. A. Dorian drove 56, 62, 68, 71, 104, and 507 mi on 6 consecutive days. B. Mandy entered pumpkins weighing 2, 8.5, 9.2, 9.8, and 10.1 lb in the contest at the county fair. C. The winning times in each of the 5 heats of the 400-meter dash were 1:01, 1:03, 1:03.4, and 1:04.9 min. D. The bakery shop sold 46, 51, 62, and 72 cupcakes on each of the last 2 Saturdays and Sundays.

Answers

Median is a better measure of center than the mean(average)

a) 56,62,68,71,104,507 ⇒ Median is a better measure. Mean is not a better measure because of the outliers.

b) 2,8.5, 9.2, 9.8, 10.1 lb ⇒ Median is a better measure.

c) Mean is a better measure. No outliers. Data set values are close with each other.

d) Mean is a better measure.

Factor completely
4a+4b+4c

Answers

$4a+4b+4c =4(a+b+c)$

All you have to do is look for what each term has in common. In this case it would be the 4. 4(a+b+c) would be your answer because that is the only thing you can take from all of the terms.

If there are 15 red tulips every 9 yellow tulips how many yellow tulips are the for every 5 tulips

Answers

Answer:

3 yellow tulips

Step-by-step explanation:

15 : 9

5 :?

45 ÷ 15 = 3 yellow tulips

Consider the following system of equations: y = −2x + 3
y = x − 5

Which description best describes the solution to the system of equations?

Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.

Line y = −2x + 3 intersects line y = x − 5.

Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.

Line y = −2x + 3 intersects the origin.

Answers

Answer:

Line $y=-2x+3$ intersects line $y=x-5$

Step-by-step explanation:

We are given that

$y=-2x+3$

$y=x-5$

Subtract one equation from other then we get

$-3x+8=0$

$3x=8$

$x=(8)/(3)$

Substitute the value of x in first equation then we get

$y=-2((8)/(3))+3=-(16)/(3)+3=-(-7)/(3)$

Hence, the solution $((8)/(3),-(7)/(3))$ is the intersection point of two line equations .

Answer:Line $y=-2x+3$ intersects line $y=x-5$

THE answer is B. Line y = −2x + 3 intersects line y = x − 5.

Explanation:

(I got it correct on the quiz)

PROOF:

In a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units. What is the length of the hypotenuse (hint: use Pythagorean Theorem)?

Answers

The length of the hypotenuse of given right triangle is 9.2 units.

Given that, in a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angledtriangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Let the length of the hypotenuse be x.

Now, using Pythagoras theorem, we get

x²=6²+7²

⇒x²=36+49

⇒x²=85

⇒x=√85

⇒x=9.2 units

Therefore, the length of the hypotenuse of given right triangle is 9.2 units.

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$hypotenuse = √(6^2+8^2)= √(36+64)= √(100)=10 \ units$