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
Nadusha1986 [10]
3 years ago
11

Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.

Mathematics
1 answer:
kari74 [83]3 years ago
7 0

Answer:

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

Step-by-step explanation:

(2x + 3)⁵

₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵

Use Pascal's triangle to find nCr.

\left\begin{array}{c}1\\1\ 1\\1\ 2\ 1\\1\ 3\ 3\ 1\\1\ 4\ 6\ 4\ 1\\1\ 5\ 10\ 10\ 5\ 1\end{array}\right

1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵

(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

You might be interested in
Factor the trinomial by grouping.<br> 9x^3 - 3x^2 -30x
katen-ka-za [31]

Answer:

3x(3x+5)(x-2)

Step-by-step explanation:

9x^3-3x^2-30x= \\\\3x(3x^2-x-10)= \\\\3x(3x^2+5x-6x-10)= \\\\3x(x(3x+5)-2(3x+5))= \\\\3x(3x+5)(x-2)

Hope this helps!

4 0
3 years ago
John put 5 identical pairs of white socks and 5 identical pairs of black socks in the dryer. If he reaches in and grabs some soc
djyliett [7]

Answer:

1/2

Step-by-step explanation:

fhbxgjhf u have it in a

7 0
3 years ago
The sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number​
KonstantinChe [14]

Answer:

670

Step-by-step explanation:

2003-814=1189

1189-519=670

8 0
3 years ago
Read 2 more answers
A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?
levacccp [35]
It will last 24 ......
4 0
3 years ago
Read 2 more answers
Please help me find the slope of the line !!
LenaWriter [7]
The slope of the line is 3/2. That would be letter B. You take two points from the graph and subtract them from each other to find the slope. Hope this helps!
3 0
3 years ago
Other questions:
  • 8th grade math ,please answer
    6·2 answers
  • Katie lunch cost 17 dollars no tax she gave a tip of 18 percent of the cost of lunch what’s the total cost no tax
    15·2 answers
  • What’s the correct answer for this question?
    9·1 answer
  • I tried x=44 and i still don’t understand even with the lesson, what does x equal?
    6·1 answer
  • What is the surface area of the square pyramid
    14·1 answer
  • Determine the surface area of this
    8·2 answers
  • X+5(x-1)=(x-3)4-1 anyone?
    9·1 answer
  • What is the area of a sector with a central angle of 255 and a radius of 18.4 m?
    8·1 answer
  • Help please please help me I really really need help
    13·1 answer
  • 4. Write a number in which the digit 2 is one tenth the<br> value of the digit 2 in 8.524.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!