$a)\left(d+1\right)\left(d^2+3d+5\right)=d^3+\underline{3d^2}+\underline{\underline{5d}}+\underline{d^2}+\underline{\underline{3d}}+5=d^3+4d^2+8d+5$  

$b)\left(8-2y\right)\left(3y^3+4y^2-y\right)=\underline{24y^3}+\underline{\underline{32y^2}}-8y-6y^4-\underline{8y^3}+\underline{\underline{2y^2}}=$  

$=16y^3+34y^2-8y-6y^4$  

$c)\left(4a^2-4a+5\right)\left(2a^2+7\right)=8a^4+\underline{28a^2}-8a^3-28a+\underline{10a^2}+35=$       

$=8a^4-8a^3+38a^2-28a+35$  

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

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