Question

[Do Thai Hung 5i6]

chứng minh các đẳng thức sau (x-y)^3 +4y(2x^2+y^2)=(x+y)^3+2y(x^2+y^2)

Answer 1

[zZz Cool Kid_new zZz]

\(\left(x-y\right)^3+4y\left(2x^2+y^2\right)=\left(x+y\right)^3+2y\left(x^2+y^2\right)\)

\(\Leftrightarrow x^3-3x^2y+3xy^2-y^3+8x^2y+4y^3=x^3+3x^2y+3xy^2+y^3+2x^2y+2y^3\)

\(\Leftrightarrow\left(-3x^2y+8x^2y\right)+3xy^2+3y^3=\left(3x^2y+2x^2y\right)+3xy^2+3y^2\)

\(\Leftrightarrow5x^2y+3xy^2+3y^2=5x^2y+3xy^2+3y^2\)