F.2 maths

Q.1
[ (6x - 3y) / (10 x^2 + xy - 3y^2) ] * (5x^2 + 8xy + 3y^2)
= { 3(2x-y) / [(2x-y) (5x+3y)] } * [(5x+3y) (x+y)]
= 3(x+y)

Q.2
I suppose you made a typo, and "20x^2" should be "20(x^2)y".
-16x^3 + 20(x^2)y - 6x(y^2)
= -2x (8x^2 - 10xy + 3y^2)
= -2x(4x - 3y)(2x - y)

Q.3
Your question is very ambiguous. I suppose you mean this:
{ [4(k^2)(x^2)(y^2) + 7k(x^2)y - 2(x^2)] / [2(k^2)x(y^2) + 7kxy + 6x] } / (4ky-1).
If so, then
{ [4(k^2)(x^2)(y^2) + 7k(x^2)y - 2(x^2)] / [2(k^2)x(y^2) + 7kxy + 6x] } / (4ky-1)
= { (x^2) [4(ky)^2 + 7ky - 2] } / { x [2(ky)^2 + 7ky + 6] (4ky - 1) }
= { (x^2) (4ky - 1) (ky + 2) } / { x (2ky + 3) (ky + 2) (4ky - 1) }
= x / (2ky + 3)

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(6x-3y/10x^2+xy-3y^2)*(5x^2+8xy+3y^2)
=3(2x-y) / (2x-y)(5x+3y)*(5x+3y)(x+y)
=3(x+y)