Expand (-2x+4)^5 using the binomial theorem (Pascals triangle)

Will award brainiest, (show work)

100 points, silly answers will be reported immediately.

Answers

Answer 1

Answer:

[tex]-32x^5+320x^4-1280x^3+2560x^2-2560x+1024[/tex]

Step-by-step explanation:

We must expand [tex](-2x+4)^5[/tex] using the Binomial Theorem.

To do so, we need Pascal's Triangle. Seeing that the exponent is 5, we look at the 5 + 1 = 6th row of Pascal's Triangle. The numbers here are:

1, 5, 10, 10, 5, 1

These will be the numbers to multiply all the distinct terms in the expansion by.

Remember that when expanding this out, we always start by taking the first term (-2x here) to the nth power (here, it's 5th power) and multiplying that by the second term (4 here) to the 0th power:

(-2x)^5 * 4^0 = -32x^5 * 1 = -32x^5

Since this is our first term, we multiply it by the first Pascal number from above: 1. Then, we simply get -32x^5 as our final first term of the expansion.

We repeat this process, each time lowering the first power by 1 and increasing the second power by 2.

2nd term:

(-2x)^4 * 4^1 = 16x^4 * 4 = 64x^4

Multiply by 5:

64x^4 * 5 = 320x^4

3rd term:

(-2x)^3 * 4^2 = -8x^3 * 16 = -128x^3

Multiply by 10:

-128x^3 * 10 = -1280x^3

4th term:

(-2x)^2 * 4^3 = 4x^2 * 64 = 256x^2

Multiply by 10:

256x^2 * 10 = 2560x^2

5th term:

(-2x)^1 * 4^4 = -2x * 256 = -512x

Multiply by 5:

-512x * 5 = -2560x

6th term:

(-2x)^0 * 4^5 = 1 * 1024 = 1024

Multiply by 1:

1024 * 1 = 1024

Hence, our expansion is:

[tex]-32x^5+320x^4-1280x^3+2560x^2-2560x+1024[/tex]


Related Questions

1.5 tenths x 20 = ______ tenths

Answers

Answer: 1.5 times 20 equals to 300

Mr. Brown bought some books at a book sale, including 4 paperback books. 20% of all the books he bought were paperbacks. How many books did Mr. Brown buy in all?​

Answers

Answer:

20 books

Step-by-step explanation:

20% is 1/5 of 100% so the other 4/5 would be 4 times 5 which equals 20 books it total

Answer:

Mr. Brown bought 20 books.

Step-by-step explanation:

20% times 5 would be 100%. Since Mr. Brown bought 4 books, and that was 20% of all the books he bought, you would have to multiply the number of paper back books by 5 to get the answer of 100% of all books he bought, which would be 20. This problem would look like this 20(5) = 4(5), 100% = 20 books.

IS IT 18, OR 27 ON EDGE

Answers

Answer:

Could we get a bit more info?

Step-by-step explanation:

helppp meeeeeeeeeeeeeeeeee kdndnd

Answers

Answer:

20

Step-by-step explanation:

hope this helped have a nice day!!

Answer: the answer is 20

what is c(4+3c)-0.75(c+3) simplified

Answers

Well I came up with the answer
3c^2 + 3.25c - 2.25

Not sure if this is correct but I hope it is and that it helps!

Have an amazing day✨❤️

Select the image set that matches the ratio 4:2

Answers

its the second option since there are 4 circles and 2 oval things.

hope this helps!! :)

There are 4 trucks for every 5 cars in a parking lot. How many trucks and cars
could be in the parking lot?
A 64 trucks and 80 cars
B 72 trucks and 73 cars
C 84 trucks and 100 cars
D 96 trucks and 110 cars

Answers

Answer:

The answer is A.

Step-by-step explanation:

I hope this helps!

HELP! please! ASAP! pleasee

Answers

Answer:

11.9

Step-by-step explanation:

I just know this off the top of my head

The real one is 11.18034

What does E stand for?

Answers

Answer:

E stands for the power of ten the number is multiplied by

I thonk

6*9+(6+9)=?

Plz I really need this in the next minute.

Answers

6*9+(6+9)= 6*9+15= 54+15=69 you have to use Pemdas

The coordinates of point A on a grld are (-3,-2), Point A is reflected across the y-axls to obtain point B. The coordinates of point B are
-2).

Answers

Answer:

The coordinates of the image of B(-3, -2) is B'(3, -2).

Step-by-step explanation:

We know that when a point (x, y) is reflected across the y-axis, the y-coordinate remains the same, and then the x-coordinate becomes negative.

i.e.

Thus, the image of P(x, y) is P' (-x, y).

Given the point

B(-3, -2)

Hence, the image of B(-3, -2):

(-x, y) → (-(-3), -2) = (3, -2)

Therefore, the coordinates of the image of B(-3, -2) is B'(3, -2).

Explain how to get it

Answers

Answer:

50

Step-by-step explanation:

let <LPM be x

60+70+x=180 (sum of angle in triangle is 180)

x=50

<LPM=<KPN (being vertically opposite angle)

<KPN= 50

Answer:

Angle NPK° = 50°

Step-by-step explanation:

in triangle MPL

60 + 70 +AngleMPL=180(Angle sum property)

Angle MPL = 180 -60-70 = 50°

Angle NPK = AngleMPL

Angle NPK = 50°

Translate the sentence into an equation.
Three times the sum of a number and 5 equals 9.
Use the variable c for the unknown number.

Answers

Answer:

3×c+5=9

Step-by-step explanation:

thats the answer ig

Answer:

3*(c+5)=9

Step-by-step explanation:

Find the value of X.

Answers

Answer:

x=16

Step-by-step explanation:

(4x+2)+(x+8)=90

5x+10=90

5x=80

x=16

2)
Un ómnibus interprovincial parte de Lima a Huacho cada 30 minutos y otro sale cada 45 minutos. ¿Cada cuántos minutos salen juntos?

Answers

Answer:

The leave together every 90 minutes

Step-by-step explanation:

The leave together every 90 minutes:

bus A : 30 + 30 + 30 = 90

bus B : 45 + 45 = 90

please help me, make sure to tell me the answer, why it is the answer, and how it is the answer

Answers

Answer:

Step One

Calculate the area of both the skating area and the spectator area.

Area = L * W

L = 4x

W = 4x

Area = 4x * 4x

Area = 16x^2

Step Two.

Find the radius of the semicircle. R = radius

From the diagram

R = The full length - the length given in the red shaded area.

R = 4x - 2x

R = 2x

Step Three

Find the area of the semicircle.

Area of a full circle = pi R^2

Area of a 1/2 circle = [tex]\frac{\pi *(2x)^2}{2}[/tex]

Area of a 1/2 circle = [tex]\frac{\pi *4*x^2}{2}[/tex]

Area of a 1/2 circle = [tex]\frac{\pi *2*x^2}{}[/tex]

Notice that the 2 in the denominator cancels in part with the 4 in the numerator.

Step Four

Find the area of the shaded area

Area of the shaded Area = Whole Area - Area of the Semi Circle.

Area of the shaded Area = 16x² - [tex]\frac{\pi *2*x^2}{}[/tex]

The answer is the upper right corner choice I think

Answer: it's the top right corner but i'm not sure.

What is the value of P(C or T)?

A.

B.

C.

D

Answers

MARK ME AS A BRAINLIST..........

The area of the basketball court under the goal is 179.25 square feet. If the cost of
the flooring for the basketball court is $8 per square foot, how much will the flooring
under the goal cost?
Dollars

Answers

Answer:

I think its $1,434

Step-by-step explanation:

Because each its 8 dollars per square foot. I multiply 179.25 to get 1,434

Good luck!!!

Answer:

1434

Step-by-step explanation:

If the cost of the flooring for the court is 8 per square foot. Multiply the area of the court under the goal by the cost per square foot Because each its 8 dollars per square foot. I multiply 179.25 to get 1,434

Is 7/15 reapeating or terminating

Answers

Answer:

It's repeating.

Step-by-step explanation:

0.46666666666

Find the equation of the circle with the given characteristics.

Center: (2, −2) Radius: 2
The solution is:

Answers

Answer:

Step-by-step explanation:

The standard form of an equation of a circle is (x - h)² + (y - k)² = r² , where (h, k) are coordinates of a center and "r" is radius.

(x - 2)² + (y + 2)² = 4

Which of the following would be the most accurate equation for the scatter plot?

Answers

i’m pretty sure it’s the 2nd option :)

Which of terms could be added to √5?

Answers

10 is the correct answer

What is the equation of the line that passes through the point (5, - 7) and has a slope of

Answers

Answer:

B,

Step-by-step explanation:

y - 7 = 3(x - 5)

y - 7 = 3x - 15

y = 3x - 8

answer is B

Please mark me brainliest if this helped,(by clicking the little crown on my answer) it helps a lot (^o^) !

Answer:

y = 4x -13

y = 4x -13Step-by-step explanation:

y= mx + b

y= mx + b m is the Slope

y= mx + b m is the Slopem = 4

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form is

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form isy = 4x -13

find the value of x of given figure and solve this question step by step plzz help question number D​

Answers

Answer:

The value of x is 15 cm

Step-by-step explanation:

#(d)

In Δ BDC

∵ ∠D is a right angle

∴ BC is the hypotenuse

∴ BD and DC are the legs of the right angle

→ By using Pythagoras Theorem

(BC)² = (BD)² + (DC)²

∵ BD = 10 cm

∵ DC = 2√11 cm

→ Substitute them in the equation above

∴ (BC)² = (10)² +(2√11)² = 100 + 44 = 144

→ Take √  for both sides

BC = 12 cm

In Δ ABC

∵ ∠B is a right angle

∴ AC is the hypotenuse

∴ AB and BC are the legs of the right angle

→ By using Pythagoras Theorem

(AC)² = (AB)² + (BC)²

∵ AB = 9 cm

∵ BC = 12 cm

AC = x

→ Substitute them in the equation above

∴ x² = (9)² +(12)² = 81 + 144 = 225

→ Take √  for both sides

x = 15 cm

The value of x is 15 cm

quentin is filling a glass that holds 1 3/4 cups of water. he is using 1/4 cup measuring cup. how many times will he have to fill the smaller measuring cup to equal 1 3/4 cups?

Answers

Answer: 7 lol

Step-by-step explanation:

The number of times he will have to fill the smaller measuring cup to equal 1 3/4 cups is 7 times.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Glass holds = 1(3/4) cups of water

One cup holds = 1/4 cup of water

Now,

The number of 1/4 cups needed to fill the 1(3/4) cups of water glass.

1/4 x C = 1(3/4)

C/4 = 7/4

C = 7/4 x 4

C = 7

Thus,

The number of times the smaller cup fills the glass is 7.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ2

True or False: Rosa has a beginning balance of $4,750 in her Checking account. After
depositing a paycheck (p), she then writes 3 checks (c), withdraw money from an ATM (a),
then gets refunded some money (r). Write an Algebraic Expression that models the
situation.
Is this the correct expression?
$4,750 + p - 3c - a +r

Answers

Answer:

true

Step-by-step explanation:

29/3 as an a mixed number

Answers

Answer:

9.6 repeating

Step-by-step explanation:

Mr. Cornapple is the fruit & vegetable buyer for a large school district. In a given week, he has a budget of $6,550. Bushels of apples cost $40 each, and bushels of corn cost $30 each. The following inequality represents the amount of money that Mr. Cornapple spends on apples and corn.

Answers

Answer:

40x + 30y ≤ 6,550

Step-by-step explanation:

Given:

Cost of each apple bushels = $40

Cost of each corn bushels = $30

Total budget = $6,550

Find:

Inequality

Computation:

Assume;

Total number of apple bushels = x

Total number of corn bushels = y

So,

40x + 30y ≤ 6,550

Write the equation of the line through (6, 1) and perpendicular to x+2y−12=0.

Answers

Using the equation- y-y0=m(x-x0)
For (x0,y0)=(6,1) and m=2

nancy earns $12.50 an hour cleaning houses, but doesn’t work on saturday or sunday. if she works from 8:00 am to 2:00 pm, how much money will she make ?

Answers

Answer:

In a day, Nancy will earn $27.50.  In a week, Nancy will earn $437.50.

Step-by-step explanation:

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