Answer:
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
============================================================
Explanation:
Let's use Pascal's Triangle
In the row that starts with 1,5,... we have the values 1,5,10,10,5,1
These will be the coefficients of the terms.
Let x = 2a and y = 2b
We want to expand out (x+y)^5
Using pascals triangle, we get the following expansion
(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5
The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.
Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.
At this point, we plug in x = 2a and y = 2b
Since this will clutter things a bit, I'll do it term by term
1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^55x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^210x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^35x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^41x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5So in the end, the expression (2a+2b)^5 expands out to
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.
Answer: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex].
Using Pascal's triangle we get:
[tex](x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5[/tex]
Here, x = 2a and y = 2b
So the terms become:
[tex]1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\[/tex]
Hence: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex]
Learn more: https://brainly.com/question/13769924
find the sum of the first 20 terms 1.5, 1.45, 1.40, 1.35
Answer: 20.5
Step-by-step explanation:
subtract 0.05 from each answer until you get 20 terms then add those terms up
HELP PLEASE ASAP!! WILL GIVE BRAINLIEST ❤️
Find the slope of the line. Enter your answer in simplest form.
Answer:
slope=4
Step-by-step explanation:
m=y2-y1/x2-x1
4-(-4)=8
5-3=2
8/2=4
hope this helps :3
if it did pls mark brainliest
Given: O ∈ AB , ON is ∠ bisector of ∠AOC, OF is ∠ bisector of ∠COB, m∠FOB=70°. Find: m∠AON
Answer:
AOC = 20 degrees
Step-by-step explanation:
We know that FOB is 70 degrees, and COF is 90 degrees. So just add 70+90 and get 160 degrees. Then you subtract that from AOB which is 20 degrees.
(first question btw)
please help i will mark brainliest if correct!
Answer:
(3,9)
Step-by-step explanation:
Because the translation moves 1 in the x direction and 4 in the y direction, you just add those to the starting x and y coordinates.
(2+1, 5+4)
(3, 9)
Which of the following values are solutions to the inequality
Please help me with this
A farmer collected 1,957 eggs from her chickens she puts them into a carton that each hold 48 eggs how many cartons will the farmer need to hold all of the eggs
Answer:
41 cartons will be needed
Step-by-step explanation:
here, we need to know the number of cartons the farmer needs to hold all the eggs
To calculate this, we simply make a division of the number of eggs by the number of eggs in a carton
That would be 1957/48 = 40.77
The closest number of cartons here is 41
Is this relation a function? Explain.
Answer:
No
Step-by-step explanation:
In a function there can only be one x for each y.
The first floor of a house consists of a kitchen, playroom, and dining room. The areas of the kitchen, playroom, and dining room are in the ratio 4 : 3 : 2 . The combined area of these three rooms is 189 square feet. What is the value of one box on the tape diagram ?
Answer:
The value of one box in the tape diagram will be 21 square feet
Step-by-step explanation:
Here, we have the total ratio added as 4 + 3 + 2 = 9
So the area of one box on the tape diagram will be the combined area divided by the total square feet
Mathematically, that will be;
189 square feet/9 = 21
Answer:
21
Step-by-step explanation:
^^^^^^
What is the correct answer for all?
Answer: 13.B
14.B
15.C
16.A
17.D
18.A
Step-by-step explanation:
What is the domain and range of these graphs ?
2x+3y=122, x, plus, 3, y, equals, 12
Complete the missing value in the solution to the equation.
((left parenthesis
,8),8)
she me he sid sud iebe Howie
7 less than the difference of 12 and 5
Answer:
the difference of 12 and 5 is 7 so it would be 0
Need help ASAP!! Tysm will mark brainliest
Answer:
about 30 then you will still fall short of that mark
HOPE IT HELP I AM NOT WANTING TO BE INCORRECT
Step-by-step explanation:
this is idiotic sense all the 3's will fall short
Find the slope plz help help plz
Answer:
-2
Step-by-step explanation:
PLEASE HELP
find the first 5 terms in the sequence
A) 6, 12, 24, 48, 96
B)1, 2, 3, 4, 5
C)6, 7, 8, 9, 10
D) 6, 11, 21, 41, 81
Answer:
The first five terms are 6, 11, 21, 41, 81 ⇒ D
Step-by-step explanation:
∵ The rule of the sequence is a(1) = 6; a(n) = 2 a(n - 1) - 1 for n ≥ 2
∴ The first term of the sequence is 6
∴ The value of n represents the position of the term
∵ n = 2
∴ a (n - 1) = a(2 - 1) = a1
∵ a1 = 6
→ Substitute a1 by 6
∴ a(2) = 2(6) - 1 = 12 - 1
∴ a(2) = 11
∵ n = 3
∴ a (n - 1) = a(3 - 1) = a2
∵ a2 = 11
→ Substitute a2 by 11
∴ a(3) = 2(11) - 1 = 22 - 1
∴ a(3) = 21
∵ n = 4
∴ a (n - 1) = a(4 - 1) = a3
∵ a3 = 21
→ Substitute a3 by 21
∴ a(4) = 2(21) - 1 = 42 - 1
∴ a(4) = 41
∵ n = 5
∴ a (n - 1) = a(5 - 1) = a4
∵ a4 = 41
→ Substitute a4 by 41
∴ a(5) = 2(41) - 1 = 82 - 1
∴ a(5) = 81
∴ The first five terms are 6, 11, 21, 41, 81
If x - 3 Is a factor P(x) = x ^ 3 - 7x ^ 2 + 15x - 9, which of the following represents the complete factorization for P(x) ?
A. (x-3)(x+4)(x+1)
B. (x-3)(x+3)(x+1)
C. (x-3(x-3)(x-1)
D. (x-3)(x+3)(x-1)
the answer is c, i just got this question
Answer: C
Step-by-step explanation:
Find the distance between (0,5) and (8,9). Round your answer to the nearest tenth.
The distance is about
units.
Answer:
8.9 units
Step-by-step explanation:
sqrt[(x2-x1)^2+(y2-y1)^2]
sqrt[8^2+4^2]
sqrt(80)
8.9 units
whats the slope and y intercept of the line: y=1/2x +2
Answer:
slope: 1/2
y-intercept: 2
Step-by-step explanation: If u go by y=mx+b, you know that m= your slope and b equals the y-intercept. so to put them together:
y=mx+b
| |
y=1/2x+2
Fred opened a bank account with $310. He then deposits $55 per week. Stan started his bank account with $650 and withdraws $30 per week. Set up an equation to represent this situation. After how many weeks, w, will their bank accounts have the same amount in them
Answer: 4 weeks
Step-by-step explanation:
PLEASE HELP WILL GIVE 20 POINTS
Use I = PRT to solve.
(time is in years)
P = $450
R = 5%
T = 7 years
Find I.
Answer:
$150.50
Step-by-step explanation:
I = 450 × 0.05 × 7 = 157.5
I = $ 157.50
The simple interest accumulated
on a principal of $ 450.00
at a rate of 5% per year
for 7 years is $ 157.50.
Hellooo :)
The answer is I = $ 157.50
Please someone please help, will mark you Brainliest
Read the problem carefully and write the required information:
Community Gym charges a $50 membership fee and a $55 monthly fee. Workout Gym charges a $200 membership fee and a $45 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will that amount be?
What are you looking for?
Define a variable:
Write the equation:
Solve the equation:
What will the amount of money be when the total amount of money paid to both gyms is the same?
Answer:
Step-by-step explanation:
Community gym
=> membership fee = $50
=> monthly fee = $55
=> First month = 105$
=> 50 + 55(x)
=> 50 + 55 (15)
=> 50 + 825
=> 875
Workout gym
=> membership fee = $200
=> monthly fee = $45
=> First month = 245$
=> 200 + 45(x)
=> 200 + 45(15)
=> 200 + 675
=> 875
On the 15th month, community gym and workout gym will both get the same amount of $875.
Answer: what are you looking for? after how many months will the total amoung of money paid to both gyms be the same? Define a variable: I'm not sure. Write the equation, community Gym 50 + 55(x), workout gym 200 + 45(x), solve the equation. on the 15th month, community gym and workout gym will both get the same amount of $875.
Step-by-step explanation:
what is the difference between 3/8 and 61/64 redosed
Answer:
Distance between points = [tex]37/64\\[/tex]
Step-by-step explanation:
This is a relatively simple problem. Here we have to find the distance between two points on the number line.
The given two numbers are fractions and to find the difference between these two numbers, we have to make their denominators common.
One has denominator as 8 and the other as 64.
We make the common denominator as 64.
Then the fractions 24/64 are 61/64 and .
The distance between the two points = 61/64 - 24/64
= 37/64
Step-by-step explanation:
HELP! GIVING OUT BRAINIEST AND 10 POINTS!!!
Answer:
i think it's 18
Step-by-step explanation:
no need to
Answer:
x=12
Step-by-step explanation:
If you add HG and GE together, you would get the value for HE. You also get HE if you add HF and FE. Setting HG+GE equal to HF+FE gives us a true equation we can use to solve for x. The math is attached.
Which expression is equivalent to -6(-2/3+2x)
-4-12x
-4+2x
4-12x
4+12x
please help!!!!!!!!!
Answer:
1) 1:100
2)200 ml
3) 1:50:100
Step-by-step explanation:
Egg to milk = 3:100 or 1:100
3:100=2:x x=200
Eggs to flour to milk=
3:150:300.
Or 1:50:100
Hope this helps plz mark brainliest :D
what is the solution to this equation? 14 - 3x = 6 - 5x
Answer:
x=-4
Step-by-step explanation:
14-3x = 6-5x
-3x -3x
14 = 6-2x
-6 -6
-2x = 8
x = -4
Hope this helped! :)
The brown family has 5 liters of lemonade. Each liters of lemonade weighs 1 kilogram. At the end of the day they have 290 grams of lemonade left. How many grams of lemonade did they drink.
Answer:
4710grams of lemonade.Step-by-step explanation:
Step one:
given data
the brown family has 5 liters of lemonade that weighs 1 kg per liter
this implies that they have 5kg of lemonade.
convert 5kg to grams we have 5*1000= 5000grams
(because 1000g is equal to 1kg)
Step two:
if at the end of the day there was 290grams left, then they drank
=5000-290
=4710
They drank 4710grams of lemonade.
Translate each expression then write the expression in factored form.
Ten times a number subtract from eighteen.
Answer:
I think the is 18-10s
Step-by-step explanation:
hope that helps
please help i will mark brainliest
Answer:
180, i already commented it but like i even looked it up a straight line is 180
Step-by-step explanation: