Question 314040

Use the distributive property.
I'll use a substitution to show you the particulars.
Let {{{u=-5x^5y}}}
{{{-5x^5y*(5x - 4xy^3 + 4y^4)=u*(5x - 4xy^3 + 4y^4)}}}
{{{-5x^5y*(5x - 4xy^3 + 4y^4)=5ux - 4uxy^3 + 4uy^4}}}
It's that easy.
Now substitute back and simplify.
{{{-5x^5y*(5x - 4xy^3 + 4y^4)=5(-5x^5y)x - 4(-5x^5y)xy^3 + 4(-5x^5y)y^4}}}
{{{-5x^5y*(5x - 4xy^3 + 4y^4)=-25x^(5+1)y +20x^(5+1)y^(3+1) -20x^5y^(4+1)}}}
{{{-5x^5y*(5x - 4xy^3 + 4y^4)=-25x^(6)y +20x^(6)y^(4) -20x^5y^(5)}}}