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
Jet001 [13]
3 years ago
7

Use the Binomial Theorem/Pascal's Triangle to expand (2a + 2b)^5

Mathematics
1 answer:
pochemuha3 years ago
8 0

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^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

So 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.

You might be interested in
Simplify the expression (0.4)^3
mafiozo [28]
0.4^3 = 0.4 · 0.4 · 0.4 = 0.064
6 0
3 years ago
Read 2 more answers
Between what two numbers would 9 be located on the number line?
oksano4ka [1.4K]
Answer is A. Because it is located between 9 and 10
4 0
3 years ago
What are the coordinates of a triangle NPQ with
Nonamiya [84]

Answer:i need help with this

Step-by-step explanation:

3 0
3 years ago
Choose all expressions that are equal to 0.75 x 0.5
aliya0001 [1]

The last three ones equal .375 which is the product of 0.75*0.5

3 0
3 years ago
Is this growth or decay? y=2*6x Brainliest to first correct answer
MissTica

Answer:

this is growth

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is the answer to Y=-1/5x-5 y=2/5x-2
    8·1 answer
  • Complete the statements about the two cones. The volumes of the cones are equal when . If a > b, then the cross-sectional are
    7·1 answer
  • Find a polynomial of degree 3 with real cofficients and zeros of -3,-1,4 for which f(-2)=24​
    13·1 answer
  • What fraction of a pound is 80p
    8·2 answers
  • 23,45 seven .9 plus 38seven .15
    6·2 answers
  • (3x-4)^2 - (2x-1) ^2​
    8·1 answer
  • Complete the square to write the equation, 4x2 + 24x – y + 43 = 0, in standard form.
    10·2 answers
  • ANY MATH EXPERTS PLS HELP RN I GOT 30 MIN LEFT I PUT 100 POINTS
    12·2 answers
  • A rule for creating a pattern is given below.
    14·1 answer
  • Look at the time on the following clocks. How much time has passed from the first clock to the second clock? The time passed is
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!