$a)5x^2.(4x^3-7x+$$\dfrac{1}{5})$
$=20x^5-35x^3+1x^2$
$b)(8x^3-6xy+7)-(-$$\dfrac{1}{2}xy)$
$=-4x^4y+3x^2y^2-$$\dfrac{7}{2}xy$
$c)(4x^2-6x+5).(2x+3)$
$=4x^2.(2x+3)-6x.(2x+3)+5.(2x+3)$
$=8x^3+12x^2-12x^2-18x+10x+15$
$=8x^3-8x+15$
$d)(4x^2+6xy+9y^2).(2x-3x)$
$=4x^2.(2x-3x)+6xy.(2x-3x)+9y^2.(2x-3x)$
$=8x^3-12x^3+12x^2y-18x^2y+18xy^2-27xy^2$
$=-4x^3-6x^2y-9xy^2$
@Nobitao@