## anonymous one year ago Use the Binomial Theorem to expand the binomial and express the result in simplified form. (5x-5y)3

1. anonymous

Help much appreciated!

2. Nnesha

$\huge\rm (a+b)^3=1a^3+3a^2b+3ab^2+b^3$

3. Nnesha

you can use pascal's triangle for the coefficient and the exponent of first term start from highest degree to 0 and the exponent of 2nd term start from 0 to highest degree |dw:1443580070541:dw| like in this example power of first term is decreasing and 2nd term exponents are increasing

4. Nnesha

make sense or no ???

5. anonymous

$15z-15y?$

6. Nnesha

the numbers in red color r from the pascal's triangle|dw:1443580345523:dw| 3rd row

7. anonymous

So in this case, you would use the third row of pascal's triangle? Since it's to the third power?

8. Nnesha

yes right

9. Nnesha

but remember it starts from 0 |dw:1443580628444:dw|

10. Nnesha

an y question ? can u solve ur question nw ??

11. anonymous

I'm still kind of confused... do you multiply the coefficients of the binomial's terms (that are being raised to a certain power), by the numbers of the specified Pascal's Triangle row?

12. Nnesha

yes in ur question there are numbers in first and term so you should multiply the coefficient by the coefficient of the term |dw:1443581219197:dw| now u should multiply the coefficient one by 5^3

13. Nnesha

$\large \rm (5x-5y)^3=\color{ReD}{1}(5x)^\color{blue}{3}(-5y)^0+\color{reD}{3}(5x)^\color{blue}{2}(-5y)^1.......+$ as u can see power of first term is decreasing andexponent of 2nd terms is increasing

14. Nnesha

-3(5x)^2(-5y)^1 = ????