Giải thích các bước giải:
a.Ta có:
$(\dfrac34x^{n+1}-\dfrac12y^n)\cdot 2xy-(\dfrac23x^{n+1}-\dfrac56y^n)\cdot 7xy$
$=(\dfrac32x^{n+1}-y^n)\cdot xy-(\dfrac{14}3x^{n+1}-\dfrac{35}6y^n)\cdot xy$
$=(\dfrac32x^{n+1}-y^n-(\dfrac{14}3x^{n+1}-\dfrac{35}6y^n))\cdot xy$
$=(\dfrac32x^{n+1}-y^n-\dfrac{14}3x^{n+1}+\dfrac{35}6y^n)\cdot xy$
$=(\dfrac32x^{n+1}-y^n-\dfrac{14}3x^{n+1}+\dfrac{35}6y^n)\cdot xy$
$=(-\dfrac{19}{6}x^{n+1}+\dfrac{29}{6}y^n)\cdot xy$
b.Ta có:
$3x^{n-2}(x^{n+2}-y^{n+2})+y^{n+2}(3x^{n-2}-y^{n-2})$
$=3x^{n-2}\cdot x^{n+2}-3x^{n-2}\cdot y^{n+2}+y^{n+2}\cdot 3x^{n-2}-y^{n+2}\cdot y^{n-2}$
$=3x^{n-2+n+2}-(3x^{n-2}\cdot y^{n+2}-y^{n+2}\cdot 3x^{n-2})-y^{n+2+n-2}$
$=3x^{2n}-y^{2n}$
