$#thanhchuc208$
\(a)\)
Ta có :
\(\left(5x^2+9xy-2y^2\right):\left(x+2y\right)\)
\(=[\left(5x^2+10xy)-(xy+2y^2\right)]:\left(x+2y\right)\)
\(=[5x\left(x+2y)-y(x+2y\right)]:\left(x+2y\right)\)
\(=\left(5x-y\right)(x+2y):\left(x+2y\right)\)
\(=5x-y\)
\(b)\)
Ta có :
\(\left(x^4-x^3y+x^2y^2-xy^3\right):\left(x^2+y^2\right)\)
\(=\left[\left(x^4+x^2y^2\right)-\left(x^3y+xy^3\right)\right]:\left(x^2+y^2\right)\)
\(=\left[x^2\left(x^2+y^2\right)-xy\left(x^2+y^2\right)\right]:\left(x^2+y^2\right)\)
\(=\left(x^2+y^2\right)\left(x^2-xy\right):\left(x^2+y^2\right)\)
\(=\left(x^2-xy\right)\)
