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
Anna007 [38]
3 years ago
11

Expand the binomial

middle" class="latex-formula"> using Pascal's Triangle. Show all workings necessary and include how to construct Pascal's Triangle.

Mathematics
2 answers:
LenKa [72]3 years ago
7 0

Answer:

Solution: x³ + 3x² + 3x + 1

Step-by-step explanation:

Take a look at the following Pascal's Triangle:

(x + y)⁰ =                                1

(x + y)¹ =                             1x + 1y

(x + y)² =                       1x² + 2xy + 1y²

(x + y)³ =                  1x³ + 3x²y + 3xy² + 1y³

(x + y)⁴ =             1x⁴ + 4x³ + 6x²y² + 4xy³ + 1y⁴

As you can see our binomial is '(x + 1)³.' Therefore we expand the expression with respect to the third row in the Pascal's Triangle, (x + y)³ = 1x³ + 3x²y + 3xy² + 1y³. The procedure would be as follows:

(x + 1)³ = 1x³ + 3(x)²1 + 3x(1)² + 1(1)³ = x³ + 3x² + 3x + 1

yan [13]3 years ago
4 0

Pascal's triangle will be shown in the image below. Since we have the binomial (x + 1)^3 (3 mean third row) take the third row and simplify.

1x^3 + 3x^2y + 3xy^2 + 1y^3

~Substitute 1 for y

x^3 + 3x^2 + 3x + 1

Best of Luck!

You might be interested in
If the number of bacteria in a
Y_Kistochka [10]

Answer:

The population of 75 hours from now would be 40,000.

Step-by-step explanation:

The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.

5 0
3 years ago
What number is 12 more than 43
Nata [24]
55. If it says 12 more, you add 12 to 43 to get 55. 
4 0
3 years ago
Read 2 more answers
I will give brainliest if you sub and stay subbed to JD Outdoors & Gaming​
NeTakaya

Answer:

hello again

Step-by-step explanation:

8 0
3 years ago
Simplify:
Dennis_Churaev [7]

Step-by-step explanation:

5^5•5 = 5^3

y^2/y= y^1 =y

a^2•a^3•a= a^6

b^5/b^7= b^-2

y^5/y^4=y

m^3•m^5•m^2=m^10

8 0
3 years ago
Find a polynomial f(x) of degree 3 with real coefficents and following zeros. -4,4i
ElenaW [278]

Answer:

f(x)=x^3 +4x^2 +16x +64

Step by step explanation:

\text{Given that,  two roots are}~ -4~ \text{and}~  4i.\\\\\text{Let,}\\\\~~~~~~~x = 4i\\\\\implies  x^2 = 16i^2~~~~~~~;[\text{Square on both sides}]\\\\\implies x^2 = -16~~~~~~~~;[i^2 = -1]\\\\\implies x^2 +16 = 0\\\\\text{So,}~ x^2 +16~ \text{ is a factor of the 3 degree polynomial}.\\ \\ \text{The polynomial is ,}\\\\ f(x) = (x+4)(x^2 +16)\\\\~~~~~~~=x^3 +16x +4x^2 +64\\\\~~~~~~~=x^3 +4x^2 +16x +64

7 0
2 years ago
Other questions:
  • In ABC, if mA = 81° and mC = 27°, then find m
    12·1 answer
  • The repair cost of a Subaru engine is normally distributed with a mean of $5,850 and a standard deviation of $1,125. Random samp
    15·1 answer
  • Analyze the graph of the function f(x) to complete the statement.
    13·1 answer
  • What is (64 p to the power of 18)to the power of 5/6?
    15·1 answer
  • What is the solution for -6x-17=19?
    8·2 answers
  • 5 5/6 divided by 3 1/6 in simplest form
    8·1 answer
  • Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximati
    8·1 answer
  • 8 + 3n ≥ 38 do yall know??? solve please
    12·1 answer
  • Pls do answer correct for brainliest
    13·2 answers
  • Solve for x<br><br> −5(-3x-3)+5x+4=-1
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!