$\text {a,}$
`y^2(4x+5xy)+6xyz+z(xy+z+4y)`
`= 4xy^2+5xy^3+6xyz+xyz+z^2+4yz`
`= 5xy^3+4xy^2+4yz+7xyz+z^2`
$\text {b,}$
`yz(x^2+4xy^2+y)+y^3(zx+4x)`
`= x^2yz+4xy^3z+y^2z+xy^3z+4xy^3`
`= x^2yz+5xy^3z+y^2z+4xy^3`
$\text {c,}$
`(6y+7xz)(8yz+6x)+(7x^2y+zy)(z+6xyz^2)`
`= 48y^2z+36xy+64xyz^2+42x^2z+7x^2yz+42x^3y^2z^2+yz^2+6xy^2z^3`
`= 49y^2z+36xy+64xyz^2+42x^2z+7x^2yz+42x^3y^2z^2+6xy^2z^3`
$\text {d,}$
`(6y+7z+8y^2)(5z+7xy)+xy^3+x^2z+zy`
`= 30zy+35z^2+40zy^2+42xy^2+49xyz+56xy^3+xy^3+x^2z+zy`
`= 31zy+35z^2+40zy^2+42xy^2+49xyz+5xy^3+x^2z`
$\text {@lamtung2007}$
