1. ## Polynomial question

According to Edward T. Dowling within Schaum's Outline of Theory and problem of Mathematical methods for business and economics:

$(3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4$

Can you clarify?

3. ## Re: Polynomial question

Originally Posted by jon80
According to Edward T. Dowling within Schaum's Outline of Theory and problem of Mathematical methods for business and economics:

$(3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4$

Can you clarify?
$(3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4$

It should be : $21x^4$ instead of $21x^2$

And it should be: $-12x^3y$ instead of $-12x^y$

The rest is correct

4. ## Re: Polynomial question

Originally Posted by psolaki
$(3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4$

It should be : $21x^4$ instead of $21x^2$

And it should be: $-12x^3y$ instead of $-12x^y$

The rest is correct
Thanks, could you show me the pattern of simplification, because when I was multiplying factor by factor the factors of my result were not adding up correctly, so I thought I might be mistaken in my approach.

5. ## Re: Polynomial question

Originally Posted by jon80
Thanks, could you show me the pattern of simplification, because when I was multiplying factor by factor the factors of my result were not adding up correctly, so I thought I might be mistaken in my approach.
What did you get when you tried? Did you follow the approach I suggested on the previous thread?

6. ## Re: Polynomial question

I did not quite understand the method of working it out by looking at your answer, sorry, would you clarify?

7. ## Re: Polynomial question

Originally Posted by jon80
I did not quite understand the method of working it out by looking at your answer, sorry, would you clarify?
You have $(3x^3- 5x^2y^2- 2y^3)(7x- 4y)$
By the "distributive law" this is the same as
$(3x^3- 5x^2y^2- 2y^2)(7x)+ (3x^3- 5x^2y^2- 2y^3)(-4y)$
Usin the distributive law again,
$(3x^3)(7x)+ (-5x^2y^2)(7x)+ (-2y^2)(7x)+ (3x^3)(-4y)+ (-5x^2y^2)(-4y)+ (-2y^3)(-4y)$
$= (21x^(3+1)- 35x^{2+1}y^2- 14xy^2)+ (-12x^3y+ 20x^2y^{2+1}+ 8y^{3+1}$
$= (21x^4- 35x^3y^2- 14xy^2)+ (-12x^3y+ 20x^2y^3+ 8y^4)$
$= 21x^4- 35x^3y^2- 12x^3y+ 20x^2y^3+ 8y^4$