Question 238621


{{{(3x-4y)(x^2-2xy+5y^3)}}} Start with the given expression.



{{{3x(x^2-2xy+5y^3)-4y(x^2-2xy+5y^3)}}} Expand.



{{{(3x)(x^2)+(3x)(-2xy)+(3x)(5y^3)+(-4y)(x^2)+(-4y)(-2xy)+(-4y)(5y^3)}}} Distribute.



{{{3x^3-6x^2y+15xy^3-4x^2y+8y^2x-20y^4}}} Multiply.



{{{3x^3-10x^2y+15xy^3+8y^2x-20y^4}}} Now combine like terms.



So {{{(3x-4y)(x^2-2xy+5y^3)}}} expands to {{{3x^3-10x^2y+15xy^3+8y^2x-20y^4}}}.



In other words, {{{(3x-4y)(x^2-2xy+5y^3)=3x^3-10x^2y+15xy^3+8y^2x-20y^4}}}.