Using proper identity, expand the following:

$(2x-y+3z)(4x^2+y^2+9z^2+2xy+3yz-6zx)$

Give possible expressions for length and breadth of the rectangle whose area is given as:

$\text{Area}=25x^2-35x+12$

Give possible expressions for length and breadth of the rectangle whose area is given as:

$\text{Area}=35x^2+13x-12$

What are the possible expressions for the dimensions of the cuboids whose volumes are Given,

$\text{Volume}=3x^2-12x$

What are the possible expressions for the dimensions of the cuboids whose volumes are Given,

$\text{Volume}=12k{y}^2+8ky-20k$

Use proper identities, factorise the following:

$4x^2+9y^2+16z^2+12xy-24yz-16zx$

Use proper identities, factorise the following:

$25x^2+16y^2+4z^2-40xy+16z-20zx$

Use proper identities, factorise the following:

$x^2+y^2+2xy+8x+8y+16$

Using proper identities, factorise the following:

$8x^3+27y^3+36x^{2}y+54x{y}^2$