[tex]4x^3-14x^2y+14xy^2-4y^3[/tex]
Explanation
[tex]2x^2-3xy+y^2\text{ multiplied by 2x-4y}[/tex]
Step 1
Apply distributive property
[tex]\begin{gathered} (2x^2-3xy+y^2)\cdot(\text{ 2x-4y)}=(2x^2-3xy+y^2)(2x)+(2x^2-3xy+y^2)(-4y) \\ (2x^2-3xy+y^2)\cdot(\text{ 2x-4y)}=4x^3-6x^2y+2xy^2-8x^2y+12xy^2-4y^3 \end{gathered}[/tex]
Step 2
Add similar terms
[tex]\begin{gathered} 4x^3-6x^2y+2xy^2-8x^2y+12xy^2-4y^3 \\ 4x^3-14x^2y+14xy^2-4y^3 \\ \end{gathered}[/tex]
then, the answer is
option D)
