SOLUTION: please give me the answers to these..THANKS! (' means exponet after..) Use Pascal's Triangle to expand each binomial. 1. (x � y5)'3 2. (2a + b)'5 3. Use the

Click here to see ALL problems on Rational-functions

Question 174368: please give me the answers to these..THANKS! (' means exponet after..)

Use Pascal's Triangle to expand each binomial.
1. (x � y5)'3
2. (2a + b)'5

3. Use the Binomial Theorem to expand (3x - 2y)4.

4. What is the coefficient of a4b6 in the expansion of (a + b)10?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Use Pascal's Triangle to expand each binomial.
1. (x � y5)'3
(x - y^5)^3
4th row of Pascal's Triangle: 1...3...3....1
Expansion: 1x^3 + 3x^2(-y^5) + 3x(-y^5)2 + 1(-y^5)^3
= x^3 -3x^2y^5 + 3xy^10 - y^15
-----------------------------------------------------
2. (2a + b)^5
6th row of Pascal: 1....6....15...20....15....6....1
Expansion: 1(2a)^5 + 6(2a)^4b + 15(2a)^3b^2 + 20(2a)^2b^3 + 6(2a)b^4 + 1b^5
= 32a^5 + 96a^4b + 120a^3b^2 + 80a^2b^3 + 12ab^4 + b^5
-----------------------------------------------------
3. Use the Binomial Theorem to expand (3x - 2y)^4.
= (3x)^4 + 4(3x)^3*4 + 6(3x)^2*4^2 + 4(3x)*4^3 + 4^4
= 81x^4 + 108x^3 + 864x^2 + 768x + 256
------------------------------------------------------
4. What is the coefficient of a4b6 in the expansion of (a + b)10?
Since 4+6 = 10 and a is to the 4 the 4th power the coefficient is 10C4 = 210
==================
Cheers,
Stan H.