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
Kay [80]
3 years ago
8

Use the Binomial Theorem to expand the binomial.

Mathematics
2 answers:
Artist 52 [7]3 years ago
4 0
<h3><u>d^3 - 4bd^2 + 16b^2d - 64d^3 is the expanded binomial.</u></h3>

The binomial theorem involves Pascal's triangle, and essentially gives you the coefficients for the formula you're going to use to expand it.

In this case, the coefficients will be 1, 3, 3, and 1.


We can set up our formula like this:

(a + (-b)) = a^3 + a^2b + ab^2 + b^3

Now we can just plug in our values:

(d + (-4b))^3 = d^3 + d^2(-4b) + d(-4b)^2 + (-4b)^3

Now, we can simplify the equation.

(d + (-4b))^3 = d^3 - 4bd^2 + 16b^2d - 64d^3

ankoles [38]3 years ago
4 0

Answer:

d^3-12d^2b+48db^2-64b^3

Step-by-step explanation:

By the binomial theorem,

(p+q)^n=\sum_{r=0}^n ^nC_r p^{n-r} q^r

Where,

^nC_r=\frac{n!}{(n-r)! r!}

Thus,

(d-4b)^3=(d+(-4b))^3=\sum_{r=0}^3 ^3C_r (d)^{3-r} (-4b)^r

=^3C_0 (d)^{3-0} (-4b)^0+^3C_1 (d)^{3-1} (-4b)^1+^3C_2 (d)^{3-2} (-4b)^2+^3C_3 (d)^{3-3} (-4b)^3

=d^3 +3(d^2)(-4b)+3(d)(16b^2)-64b^3

=d^3-12d^2b+48db^2-64b^3

You might be interested in
Please help. Whats the algebraic expression for: The quotient of 5 and twice a number
Stolb23 [73]

Answer:

5/2x

(5 divided by 2 times (twice) a number)

("x" is considered as the unknown number)

Hope this helps

:)

3 0
3 years ago
Read 2 more answers
In the first round of a local tennis tournament, there are 25 matches. Find the number of matches
LiRa [457]
There are 25 matches
5 0
3 years ago
Read 2 more answers
I need the full answers can anyone help
irina [24]

Answer:

Look it up

Step-by-step explanation:

You can look at the questions online

5 0
3 years ago
Whats 7/12 divided by 2
mel-nik [20]

Answer:

7/24

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
In comparison to 1/3 where would 2/6 be located an on a number line
marta [7]

Answer:

If you simplify 2/6, you get 1/3 by dividing the numerator and denominator by 2.

Therefore, 1/3 and 2/6 would be the same point on the number line.

3 0
3 years ago
Other questions:
  • 1.
    12·1 answer
  • PLEASE HELP!!
    15·1 answer
  • 120-3/4y=60 solve for y
    9·1 answer
  • PLEASE HELP!!!
    11·2 answers
  • Find a “solution” for an equation with two variables. Tell me an x, y ordered pair that is a solution (answer) for this equation
    15·1 answer
  • If something cost $3.50 and you give them $10. what is your change?
    13·2 answers
  • What is the value of 280
    13·1 answer
  • What is the answer and steps to the following equation: 6(4-z)=2z
    11·2 answers
  • 36 slices from 4 cakes = slices per cake
    8·2 answers
  • ______________ can hold multiple values within a single variable and is defined by having values between square brackets.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!