Rút gọn biểu thức: 1/4 (2x^2+ y) ( x^2- 2y^2) + 1/4 ( 2x^2- y) ( x^2+ 2y^2)

Trả lời

$\frac{1}{4}\left(2x^2+y\right)\left(x^2-2y^2\right)+\frac{1}{4}\left(2x^2-y\right)\left(x^2+2y^2\right)$

$=\frac{1}{4}\left(2x^4+x^{2}y-4x^2{y}^2-2y^3\right)+\frac{1}{4}\left(2x^4-x^{2}y+4x^2{y}^2-2y^2\right)$

$=\frac{1}{2}{x}^4+\frac{1}{4}{x}^{2}y-x^2{y}^2-\frac{1}{2}{y}^3+\frac{1}{2}{x}^4-\frac{1}{4}{x}^{2}y+x^2{y}^2-\frac{1}{2}{y}^2$

$=\left(\frac{1}{2}{x}^4+\frac{1}{2}{x}^4\right)+\left(\frac{1}{4}{x}^{2}y-\frac{1}{4}{x}^{2}y\right)+\left(x^2{y}^2-x^2{y}^2\right)-\frac{1}{2}{y}^3-\frac{1}{2}{y}^2$

$=x^4-\frac{1}{2}{y}^3-\frac{1}{2}{y}^2$