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

Guest Jun 6, 2014

Best Answer 

 #1
avatar+5454 
+29

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)

kitty<3  Jun 6, 2014
 #1
avatar+5454 
+29
Best Answer

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)

kitty<3  Jun 6, 2014
 #2
avatar+27217 
+8

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. 

Alan  Jun 6, 2014
 #3
avatar+94083 
+8

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.$$

Melody  Jun 6, 2014
 #4
avatar+92367 
+3

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

 

CPhill  Jun 6, 2014
 #5
avatar+94083 
+3

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

Melody  Jun 6, 2014
 #6
avatar+92367 
+3

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

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

 

CPhill  Jun 6, 2014
 #7
avatar+94083 
+3

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?  

Melody  Jun 6, 2014
 #8
avatar+5454 
+26

Of course, Melody CPhill is always cool!

kitty<3  Jun 7, 2014

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