Đáp án:
`1)` ` (4xy-{yz}/2).\ (-5/3 xy^2)`
`={-20}/3x^2y^3+5/6xy^3z`
`2)` `x^{n-1}(x+y)-y(x^{n-1}+y^{n-1})=x^n-y^n`
Giải thích các bước giải:
`1)` Ta có:
`\qquad (4xy-{yz}/2).\ (-5/3 xy^2)`
`=4xy\ .\ (-5/3xy^2)-{yz}/2 . (-5/3xy^2)`
`=4.(-5/3) x.x.y.y^2-1/ 2 . (-5/3).x.y.y^2.z`
`={-20}/3x^2y^3+5/6xy^3z`
Vậy ` (4xy-{yz}/2).\ (-5/3 xy^2)`
`={-20}/3x^2y^3+5/6xy^3z`
$\\$
`2)` `x^{n-1}(x+y)-y(x^{n-1}+y^{n-1})`
`=x^{n-1}.x+x^{n+1}.y-y x^{n-1}-y.y^{n-1}`
`=x^{n+1+1}+(x^{n-1}y-x^{n-1}y)-y^{1+n-1}`
`=x^n+0-y^n=x^n-y^n`
Vậy: `x^{n-1}(x+y)-y(x^{n-1}+y^{n-1})=x^n-y^n`