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

[toyjoha]

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?

 

[Also sprach Zarathustra]

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

 

[Jameson]

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).

 

[HallsofIvy]

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.

 

[CellCoree]

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.