1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anon25 [30]
3 years ago
12

How does the Binomial Theorem’s use Pascal’s triangle to expand binomials raised to positive integer powers?

Mathematics
1 answer:
MrMuchimi3 years ago
5 0

Answer:

There are  ways for quickly multiply out a binomial that's being raised by an exponent. Like

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = (a + b)(a + b)2 = (a + b)(a2 + 2ab + b2) = a3 + 3a2b + 3ab2 + b3

and so on and so on

but there was this mathematician named Blaise Pascal and he found a numerical pattern, called Pascal's Triangle, for quickly expanding a binomial like the ones from earlier. It looks like this

1                           1      

2                   1     2     1

3                1     3     3   1

4           1     4     6     4     1

5       1     5     10     10     5     1

Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n, where n is the row of the triangle.

Hope this helps!

You might be interested in
In the xy-plane, the graph of function f(x) has zeros at −5, −2, and 2. Write the polynomial function.
Alona [7]

Answer:

f(x) = x^3 +5x^2-4x-20

Step-by-step explanation:

Given

Zeros: -5,-2,2

Required

The polynomial function

If a function has a, b and c as its zeros, the function is:

f(x) = (x - a)(x - b)(x - c)

So, we have:

Zeros: -5,-2,2

f(x) = (x - (-5))(x - (-2))(x - 2)

Open the inner brackets

f(x) = (x +5)(x +2)(x - 2)

Expand the difference of two squares

f(x) = (x +5)(x^2 - 4)

Expand

f(x) = x^3 +5x^2-4x-20

4 0
3 years ago
I need help with this my guys !
luda_lava [24]

Answer:

1/2

Step-by-step explanation:

Slope = rise/run

Rise=1

Run=2

Rise/run=1/2

4 0
3 years ago
Read 2 more answers
Of the flowers in Bella’s garden, 9/12 are tulips. What percent of the flowers in the garden are not tulips? A: 75 B: 25 C: 30 D
Amiraneli [1.4K]
9/12 as a percentage is equal to 75%.
7 0
3 years ago
Manas receives a commission of Rs.5,000 on sales of Rs.65,000.How much commission will he get on sales of Rs.20,000.
tangare [24]

\\
\text{Let Manas receives a commission of Rs. 5000 on sales of Rs. 65000}\\
\\
\text{We need to find how much commision he will get on the sale of Rs.20000}\\
\\
\text{To find the commision, we use the unitary method.}\\
\\
\text{On sales of Rs. 65000, Manas receives a commision of}=5000\\
\\
\text{so on sales of Rs. 1, Manas will receiv a commision of}=\frac{5000}{65000}\\
\\
\text{Hence on sales of Rs. 20000, Manas will receiv a commision of}\\
\\=\frac{5000}{65000}\times 20000\\
\\
=1538.46

Hence, on the sales of Rs. 20000, Manas will receive a commission of: Rs. 1538.46

6 0
3 years ago
A cable pole casts a shadow that is 12 feet long . If a 6ft tall man casts a shadow thats is 4 feet long how tall is the cable p
shepuryov [24]

Answer:

18ft

Step-by-step explanation:

6ft -> 4ft shadow

6 = 4m

m = 6/4

y = 12m

y = 12(6/4)

y = 18ft

4 0
3 years ago
Other questions:
  • #5! I originally thought this was 48 units but i am confused..can someone help me out?
    13·1 answer
  • WILL GIVE BRAINLIEST IF UR RIGHT!! PLEASE HELP!!
    6·1 answer
  • Mike,Marco,Amy,Valeria,Jeslyn,Karina,Melanie,Maria,Sonia,Edgar,Emmanuel,Joey,Anthony,Perla,David,Mia,Dominic,Isabella,Alex,Nancy
    5·1 answer
  • I need help asap 9.52 divided by 4
    6·2 answers
  • PLS HLEP ME THIS IS DUE SO SOON IM FREAKING OUTㅠㅠㅠㅠㅠㅠㅠㅠANSWER BOTH PLSSSSSS
    13·2 answers
  • An equation of a line perpendicular to the line represented by the equation y = -
    10·2 answers
  • A 16-ounce of shampoo cost $4.69. What is the price per ounce, rounded to the nearest cent
    5·1 answer
  • Which inequality is graphed on the number line? HELP PLZZZ
    13·2 answers
  • Which two expressions are equivalent?
    11·1 answer
  • A large plastic bucket is in the shape of a right, circular cylinder with dimensions shown below. If there are volume of this cy
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!