Question 111572

{{{(x^2+2xy-y^2)(3x^2-xy-2y^2)}}} Start with the given expression




{{{x^2(3x^2-xy-2y^2)+2xy(3x^2-xy-2y^2)-y^2(3x^2-xy-2y^2)}}} Expand the expression. Remember for something like {{{(a+b+c)(d+e+f)}}} it expands to {{{a(d+e+f)+b(d+e+f)+c(d+e+f)}}}



{{{(x^2)*(3x^2)+(x^2)*(-xy)+(x^2)*(-2y^2)+(2xy)*(3x^2)+(2xy)*(-xy)+(2xy)*(-2y^2)+(-y^2)*(3x^2)+(-y^2)*(-xy)+(-y^2)*(-2y^2)}}} Distribute



{{{3x^4-x^3y-2x^2y^2+6x^3y-2x^2y^2-4xy^3-3y^2x^2+y^3x+2y^4}}} Multiply



{{{3x^4+5x^3y-7x^2y^2-3xy^3+2y^4}}} Combine like terms




So {{{(x^2+2xy-y^2)(3x^2-xy-2y^2)}}} expands and simplifies to {{{3x^4+5x^3y-7x^2y^2-3xy^3+2y^4}}}.


In other words, {{{(x^2+2xy-y^2)(3x^2-xy-2y^2)=3x^4+5x^3y-7x^2y^2-3xy^3+2y^4}}}