Binomial Expansion Part I: Find Formula for 8th Power - 65 chars

In summary, the binomial expansions for (x + y)^8, (w + z)^8, (x - y)^8, and (2a + 3b)^8 were provided. The formula for (x + y)^8 can be used to find the values of (w + z)^8, (x - y)^8, and (2a + 3b)^8 by substituting specific values for x and y. For (w + z)^8, x would be equal to w and y would be equal to z. For (x - y)^8, x would stay the same while y would become -y. And for (2a + 3b)^8, x would
  • #1
toyjoha
1
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Part I. Write out the binomial expansion for each binomial raised to the 8th power.
1. (x + y) 2. (w + z) 3. (x - y) 4. (2a + 3b)
Part II. Now explain how your answer for #1 could be used as a formula to help you answer each of the other items. In each case, for #2, 3 and 4, tell what would x equal and what would y equal.

I did the binomial expansions. Those are easy, but how can you find the value?
 
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  • #2
toyjoha said:
Part I. Write out the binomial expansion for each binomial raised to the 8th power.
1. (x + y) 2. (w + z) 3. (x - y) 4. (2a + 3b)
Part II. Now explain how your answer for #1 could be used as a formula to help you answer each of the other items. In each case, for #2, 3 and 4, tell what would x equal and what would y equal.

I did the binomial expansions. Those are easy, but how can you find the value?
http://lmgtfy.com/?q=binomial+coefficient
 
  • #3
What did you get for the expansion of (x+y)^5? What happens when you substitute another term for x and y, say x=3c and y=2d into the expansion of (x+y)^5? Remember when you substitute you must pay close attention to apply any powers to the whole term, not just the variable. So if you see x^5 and you substitute x=3c, then the substituted expression would be (3c)^5, NOT 3(c^5).
 
  • #4
toyjoha said:
Part I. Write out the binomial expansion for each binomial raised to the 8th power.
1. (x + y) 2. (w + z) 3. (x - y) 4. (2a + 3b)
Part II. Now explain how your answer for #1 could be used as a formula to help you answer each of the other items. In each case, for #2, 3 and 4, tell what would x equal and what would y equal.

I did the binomial expansions. Those are easy, but how can you find the value?
They are not asking for "values". To use your answer to (1) to get (2) let x= w and let y= z. Similarly for (3) x stays x but y becomes -y. Finally, for (4) let x= 2a, y= 3b.
 
  • #5


The formula for the binomial expansion of (x + y)^8 is (x^8 + 8x^7y + 28x^6y^2 + 56x^5y^3 + 70x^4y^4 + 56x^3y^5 + 28x^2y^6 + 8xy^7 + y^8). This formula can be used to find the values of x and y in the other binomial expansions by substituting the values for x and y in the original expansion with the values given in the other expansions. For example, for (w + z)^8, x would be replaced with w and y would be replaced with z. Similarly, for (x - y)^8, x would be replaced with x and y would be replaced with -y. For (2a + 3b)^8, x would be replaced with 2a and y would be replaced with 3b. This allows for a quick and easy way to find the binomial expansion for any given binomial raised to the 8th power.
 

1. What is binomial expansion?

Binomial expansion is a mathematical process that involves finding the coefficients of a binomial raised to a certain power. It is used to simplify expressions and solve equations in algebra and calculus.

2. What is the formula for expanding a binomial to the 8th power?

The formula for expanding a binomial (a+b) to the 8th power is (a+b)^8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + b^8.

3. How do you find the coefficients in a binomial expansion?

The coefficients in a binomial expansion can be found using the Pascal's triangle or the binomial theorem. The Pascal's triangle involves adding the numbers above to get the number below, and the binomial theorem involves using combinations and factorials to find the coefficients.

4. What is the significance of the 8th power in binomial expansion?

The 8th power in binomial expansion represents the number of terms in the expanded expression. In this case, there are 9 terms (including the 0th term) in the expansion of (a+b)^8, which can be found by adding 1 to the power (8+1=9).

5. How is binomial expansion used in real-world applications?

Binomial expansion is used in various fields such as finance, physics, and biology. It can be used to model population growth, calculate compound interest, and solve equations in projectile motion and thermodynamics. It also has applications in genetics and probability theory.

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