Question

Which of the following are factors of $(x^{2}y-x{y}^2{)}^2$?​​​​

• A. $x^2{y}^2$
• B. $x^2-2xy+y^2$
• C. $x^2+2xy+y^2$
• D. $x^2+y^2$

Answer 1

Answer: (A), (B)

The correct options are
A $x^2{y}^2$
B $x^2-2xy+y^2$

We know, $(a-b{)}^2=a^2-2ab+b^2$.
Using the above identity to expand the given expression, we get,
$(x^{2}y-x{y}^2{)}^2=(x^{2}y{)}^2-(2\times x^{2}y\times x{y}^2)+(x{y}^2{)}^2=x^4{y}^2-2x^3{y}^3+x^2{y}^4=x^2{y}^2(x^2-2xy+y^2)$