use the binomial theorem to expand the binomial (x+7y)^3 and simplyfy

For this problem, you can use Pascal's Triangle as a shortcut (http://mathematics.laerd.com/maths/binomial-theorem-intro.php), but you can also expand the long way:

(x+7y)³

= (x+7y) (x+7y) (x+7y)

= (x² + 7xy + 7xy + 49y²) (x+7y)

= (x² + 14xy + 49y²) (x + 7y)

= (x³ + 14x²y + 49xy² + 7x²y + 98xy² + 343y³)

= (x³ + 21x²y + 147xy² + 343y³)

The binomial theorem (for a cubic expansion) says:

(a + b)³ = a³ + 3a²b +3ab² + b³ 

If you substitute x for a, and 7y for b in this you should get the result shown by kitty<3. 

Hi kitty,

I'm sure your answer is correct - you rarely get any wrong - but that is not a binomial expansion.

$$(x+7y)^3= (7y)^3+3*(7y)^2(x)+3*(7y)(x^2)+(x)^3 And you can take it from there.$$

Actually, Melody, I think kitty<3 got exactly the same answer you did. She just took the coefficients to their "powers."

Yes, I know Kitty got it right.  She almost never gets anything wrong!

But the question specifically asked the answerer to use the binomial theorem

If anyone want to have a look at the binomial theorum this clip seems pretty reasonable.

https://www.youtube.com/watch?v=1pSD8cYyqUo

Oh, yes....I see now....she actually "cheated," didn't she???.......

Shame on you, kitty<3 !!!!!!!!   (LOL!!!)

No she didn't "cheat" I doubt Kitty has ever heard of binomial expansions.

Shame on you Chris.  Never mind you are still cool with us.  Isn't he Kitty?  

Of course, Melody CPhill is always cool!