Use the Binomial Theorem to expand the binomial. SHOW STEPS
(d-4b)^2

Some one please help!!!

Answers

Answer 1

The binomial theorem says

[tex]\displaystyle (a + b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k \\\\(a+b)^n= \binom n0 a^n + \binom n1 a^{n-1}b + \cdots + \binom n{n-1} ab^{n-1} + \binom nn b^n[/tex]

where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient. The binomial coefficients follow a neat pattern called Pascal's triangle:

1

1   1

1   2   1

1   3   3   1

1   4   6   4   1

where the n-th row, starting with n = 0, lists the coefficient of the k-th term in the sum (with 0 ≤ k ≤ n). For example,

[tex]\displaystyle n=0 \implies (a + b)^0 = \sum_{k=0}^0 \binom nk a^{0-k} b^k = \binom00 a^{0-0} b^0 = \underline{1}[/tex]

[tex]\displaystyle n=1 \implies (a + b)^1 = \sum_{k=0}^1 \binom 1k a^{1-k} b^k = \binom10 a^{1-0} b^0 + \binom11 a^{1-1}b^1 = \underline{1}a + \underline{1}b[/tex]

[tex]\displaystyle n=2 \implies (a + b)^2 = \sum_{k=0}^2 \binom 2k a^{2-k} b^k = \binom20a^{2-0}b^0+\binom21a^{2-1}b^1+\binom22a^{2-2}b^2 = \underline{1}a^2 + \underline{2}ab+\underline{1}b^2[/tex]

Each row starts and ends with 1, and every coefficient in between is obtained by adding the coefficients directly above and to the left. The next row, for instance, would be

1   1 + 4   4 + 6   6 + 4   4 + 1   1

or

1   5   10   10   5   1

which is to say,

[tex]\displaystyle (a + b)^5 = \underline{1}a^5+\underline{5}a^4b+\underline{10}a^3b^2+\underline{10}a^2b^3+\underline{5}ab^4+\underline{1}b^5[/tex]

In your case, we have (d - 4b)², so we take a, b, and n above with d, -4b, and 2, respectively:

[tex]\displaystyle (d - 4b)^2 = \sum_{k=0}^2 \binom 2k d^{2-k} (-4b)^k[/tex]

[tex]\displaystyle (d - 4b)^2 = \sum_{k=0}^2 \binom 2k (-4)^k d^{2-k} b^k[/tex]

[tex]\displaystyle (d - 4b)^2 = \binom20 (-4)^0 d^{2-0} b^0 + \binom21 (-4)^1 d^{2-1} b^1 + \binom22 (-4)^2 d^{2-2} b^2[/tex]

[tex]\displaystyle (d - 4b)^2 = 1\cdot1\cdot d^2\cdot1 + 2 \cdot (-4) d \cdot b + 1 \cdot 16 \cdot 1 \cdot b^2[/tex]

[tex]\boxed{(d - 4b)^2 = d^2 - 8bd + 16b^2}[/tex]


Related Questions

Pleaseeeeee I need help!

THANK YOU

Answers

[tex] \: \: \: \: \: \: \: [/tex]

[tex] \frac{3}{10} \\ \\ or \: in \: alternate \: \: form \\ \\ 0.3[/tex]

refer to the attachment for explanation

hope it helps
You need to multiply across so numerator times numerator and denominator times denominator!

What +1/16 = 3/2 answer please

Answers

Answer:

1   7/16

Step-by-step explanation:

What is the radical form of the expression 4 3/2

Answers

The last option. The top part of the fraction becomes s the exponent of the number inside the root. And the bottom part of the fraction is on top part of the root symbol. With square roots you don’t write the number 2. That’s why there is no number in the last option because that means it is square root (2)

Which expression has the greatest value when c = 7? 12 - 2C 0R C - 5
please show working

Answers

If c = 7, then

12 - 2c

= 12 - 2(7)

= 12 - 14

= -2

c - 5

= (7) - 5

= 2

=》+2 > -2.

So, c - 5 has greater value than 12 - 2c, if c = 7.

______

Hope it helps ⚜

a homeowners association charges a 4.65 fee for each day your payment is late if a bill was originally 103.55 and paid 22 days late then how much is owed to the home owners?

Answers

Answer:

207.1

Step-by-step explanation:

4.65×22=102.3

103.55+102.3= 207.1

Write the equation of the line in fully simplified slope-intercept form.

Answers

Answer:

y=5/6x+5

Step-by-step explanation:

Just ask!

Hope this helps.

Sorry if I'm wrong.

~Happy Holidays!!~ o(* ̄▽ ̄*)ブ

What is the solution for -10 < x - 9?

x > -19
x < -1
x < -19
x > -1

Answers

Answer:

  x > -1

Step-by-step explanation:

Add 9 to both sides of the inequality.

  -10 +9 < x -9 +9

  -1 < x

In the form of the answers, ...

  x > -1

The solution for the given inequality is x > -1. The correct option is the last option x > -1

Linear inequalities

From the question, we are to determine the solution for the given inequality

The given inequality is -10 < x - 9

To solve an inequality, we will solve for the variable. The variable here is x

The inequality can be solved as follows

-10 < x - 9

Add 9 to both sides

-10 +9 < x - 9 + 9

Simplifying

-1 < x

Now, if -1 < x

Then,

x > -1

Hence, the solution for the given inequality is x > -1. The correct option is the last option x > -1

Learn more on solving Linear inequalities here: https://brainly.com/question/246993

1cm
1
6 cm
Diagram NOT
accurately drawn
Scm
11 cm
9 cm
| 6cm
18 cm
The diagram shows a shape.
All of its corners are right angles.
Work out the area of the shape.

Answers

Answer:

110cm²

Step-by-step explanation:

*Diagram is ALSO not accurately drawn

18cm-6cm-5cm=7cm

11cm-9cm=2cm

Area:

11cm×6cm=66cm²

7cm×2cm=14cm²

6cm×5cm=30cm²

Area of the shape:

66cm²+14cm²+30cm²=110cm²


Can you help me i Don’t understand

Answers

Answer:

  A.  {-1, 2, 7}

Step-by-step explanation:

For a set of ordered pairs, the domain is the set of first-numbers (x). The range is the set of second numbers (y, or g(x)).

The first step here is to find the g(x) values for each of the listed x-values.

The attachment shows a table.

Often, we like to list the domain and/or range values in numerical order, eliminating any duplicates. That is, the set of range values {2, -1, -1, 7} would be listed as ...

  {-1, 2, 7} . . . . . . matches choice A

_____

You find the g(x) values by substituting for x and doing the arithmetic.

  g(-2) = (-2)² -2 = 4 -2 = 2, for example

PLEASE HELP!!!
A golfer hits a ball with an initial velocity of 32.7 m/s from the ground. Find the following (round all answers to 2 decimal places...no units):

When does the ball hit the ground? ___

What is the highest height the ball goes? ___

When does the ball reach its max height? ___

How high is the ball after 4.3 seconds? ___

When is the ball 24 meters off the ground? ___ and ___ (enter the smaller value first)

Answers

Answer: 1. it doesnt since the velocity is so high, it will land in the water.

2. the ball goes about 500 feet in the air.

3. the ball reaches its max height when it starts to go down

4. the ball is at 250 since it takes 8.6 seconds for it to reach 500 feet

Step-by-step explanation:

To repair a roof that is 4 meters high Mr. Jeff leans a 5-meter ladder against the side of the building. To reach the roof how far away from the building should he place the base of the ladder?

Answers

hi have a good day.

I think correct answer is-3

A rectangle has an area of 35x + 42 square units. If the
width of the rectangle is 7 units, what is the length of the
rectangle?

Answers

Answer:

length = 5x + 6

Step-by-step explanation:

35x + 42 = 7*L    since area of a rectangle is length * width

(35x + 42) divide by 7  =  7L divide by 7

5x +6 = y

What is 8,024.62 in words?

Answers

Answer:

eight thousand twenty four sixty two hundreths

Step-by-step explanation:

you can replace the decimal pint with an and so that its

eight thousand twenty four and sixty two hundreths

Answer: eight thousand twenty-four and sixty-two hundredths

Step-by-step explanation:

What is the length of the longest side of an isosceles triangle with leg lengths 2x+12 and 5x-9 and base length 6x-2?

Answers

Your longest length is going to be 40

1/3x^2 = -3

The solution to the equation is ___?

A) x = 3
B) x = -3
C) x = ±3
D) no solution

Answers

[tex] \frac{1}{3} {x}^{2} = - 3 \\ = > {x}^{2} = - 3 \times 3 \\ = > {x}^{2} = - 9 \\ = > {x} = \sqrt{ - 9} \\ = > x = ±3[/tex]

Answer:

C) x = ±3

Hope you could get an idea from here.

Doubt clarification - use comment section.

Factorize
A) [tex]x^{2} -x-132[/tex]
B) [tex]9t^{2} -u^{2}[/tex]
C) [tex]4p^{2} -9[/tex]
D)[tex]162-8t^{2}[/tex]
E) [tex]p^{2} x-4q^{2} x[/tex]

Answers

Answers are highlighted. Hope this helps

i dont know how to do this stuff
im choosing brainliest

Answers

Answer:

5 - 15 = -10

Step-by-step explanation:

Answer:

5 - 15 = -10

Step-by-step explanation:

If you start with 5 and then subtract 15, you end up at -10.

10 is 20% of (blank)

Answers

Answer:

50

Step-by-step explanation:

Find the slope given the the two points

Answers

Answer:

the answer is 2

Step-by-step explanation:

use the slope equation

y^1-y^2/x^1-x^2

-1-(-5)/1-(-1)

4/2

2

9(2x129) = ?
Please help me im suffering math is hard

Answers

Answer:

18x^129

Step-by-step explanation:

Answer: That would be 2,322!

Step-by-step explanation:

A line graph titled If the election were held today, whom would you vote for? It shows Weeks until election on the x axis from 6 to 1 and percentage of voters on the y axis. Line labeled Diaz starts at 34 on 6, to 30 on 4, 34 on 3, 35 on 2, 38 on 1. Line labeled Smith starts at 32 on 6, to 35 on 4, 34 on 3, 33 on 2, 34 on 1. How can media coverage of polling influence the outcome of an election? Check all that apply. Voters are less informed about the potential outcome of the election. Candidates learn more about their standing. Voters may be more or less motivated to support a candidate. Candidates are less informed about voter desires. Campaigns are more able to predict election outcomes.

Answers

Answer:

2,3,5 or B,C,E

Step-by-step explanation:

Probs too late but I got it right on edge. Hope this helps anyone else :)

Please solve on same Kind of coordinate plane. Thank you!

Answers

Answer:

(0,8)

Step-by-step explanation:

In the table adam recorded the miles he travled each day while traveling from Florida to California. Calculate the average rate of change between day 4 and day 6.

Table:

End of day Distance
1 383
2 682
3 1132
4 1503
5 1906
6 2196

Answers: A) 231 Miles
B) 290 Miles
C) 347 Miles
D) 440 Miles

Answers

Hi!

To calculate the rate of change between days 4 and 6, we simply take those points, (4, 1503) and (6, 2196) and use the equation in the picture below:

Now, when we plug it in the equation, it looks like this:

[tex]\frac{2196-1503}{6-4} = \frac{693}{2} = 346.5[/tex]

Therefore, your answer is 346.5 or, rounded, 347.

Meaning, your answer is C

Hope this helps and have a great day! :D

30,098 / 6

Quotient and Remainder

Answers

Answer:

5,016.33333333

Step-by-step explanation:

divide

Kate is 11 45
years old. Karina is 1 16
years younger than Kate and Jane is 1 13
years younger than Karina. How old is Jane?

Answers

Kate-1145
Karina-1029
Jane-916

Please show step by step need it now

Answers

Answer:

x = 6+3y

y = y (any number)

the rest should follow the same steps

Step-by-step explanation:

2x-6y=12 -> divide both sides by 2 (GCF)

x-3y = 6 -> solve for x, because it has 1 as its coefficient, or the lowest coefficent

x = 6+3y

-5x+15y=-30 -> divide both sides by 5

-1x+3y=-6 -> plug in x from previous equation

-(6+3y) + 3y = -6

-6-3y+3y = -6

y = y

Which value of k makes 5-k + 12 = 16 a true statement? Choose 1 answer. А k = 1 B k = 2 k = 3 k=4
PLEASE HELP ME AND SAVE MY LIFEE
ILYYY​

Answers

Answer:

option A

K = 1

is the answer.

hope it helps

A. Would be the answer

What is the slope of a line that contains the point
(3,7) and has a y-intercept of 1?

Answers

The slope is 2
Hope this helps!

Which expression is equivalent to [(2a-3b4)2(3a5b)-2]-1 ? Assume a =/ 0, b =/ 0

Answers

Answer: The Third option

Step-by-step explanation:

1/36a^4b^10

Hope this is right!

The expression equivalent to the given expression is 1/36a⁴b¹⁰. Therefore, option C is the correct answer.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is ((2a⁻³b⁴)²/(3a⁵b)⁻²)⁻¹.

Now, ((2²a⁻⁶b⁸)/(3⁻²a⁻¹⁰b⁻²))⁻¹

= (2⁻²a⁶b⁻⁸)/(3²a¹⁰b²)

= (a⁶)/(3²2²a¹⁰b²b⁸)

= 1/36a⁴b¹⁰

Therefore, option C is the correct answer.

To learn more about an equivalent expression visit:

https://brainly.com/question/28170201.

#SPJ7

How do you work out the problem x+3=4+x

Answers

Answer:

No solution

Step-by-step explanation:

Since both x's are positive, there's no way to put to x on either side, because when you transfer sides, you add/subtract the opposite, so there can't be a value for x

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