$$ (x-y)(3 x-2 x y+4) $$ 5. $$ (7 m-3 n)\left(5 m^{2}-2 m n-7 n^{2}\right) $$ 7. $$ (2 x-y)\left(4 x^{2}+2 x y-y^{2}\right) $$ 9. $$ (4 m-n)\left(2 m^{2}-3 m n-n^{2}\right) $$

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Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(x-y\right)\left(3x-2xy+4\right)$$
- step1: Apply the distributive property:
  $$x\times 3x-x\times 2xy+x\times 4-y\times 3x-\left(-y\times 2xy\right)-y\times 4$$
- step2: Multiply the terms:
  $$3x^{2}-2x^{2}y+4x-3yx-\left(-2y^{2}x\right)-4y$$
- step3: Remove the parentheses:
  $$3x^{2}-2x^{2}y+4x-3yx+2y^{2}x-4y$$
Expand the expression $$ (7 m-3 n)(5 m^{2}-2 m n-7 n^{2}) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(7m-3n\right)\left(5m^{2}-2mn-7n^{2}\right)$$
- step1: Apply the distributive property:
  $$7m\times 5m^{2}-7m\times 2mn-7m\times 7n^{2}-3n\times 5m^{2}-\left(-3n\times 2mn\right)-\left(-3n\times 7n^{2}\right)$$
- step2: Multiply the terms:
  $$35m^{3}-14m^{2}n-49mn^{2}-15nm^{2}-\left(-6n^{2}m\right)-\left(-21n^{3}\right)$$
- step3: Remove the parentheses:
  $$35m^{3}-14m^{2}n-49mn^{2}-15nm^{2}+6n^{2}m+21n^{3}$$
- step4: Subtract the terms:
  $$35m^{3}-29m^{2}n-43mn^{2}+21n^{3}$$
Expand the expression $$ (4 m-n)(2 m^{2}-3 m n-n^{2}) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(4m-n\right)\left(2m^{2}-3mn-n^{2}\right)$$
- step1: Apply the distributive property:
  $$4m\times 2m^{2}-4m\times 3mn-4mn^{2}-n\times 2m^{2}-\left(-n\times 3mn\right)-\left(-n\times n^{2}\right)$$
- step2: Multiply the terms:
  $$8m^{3}-12m^{2}n-4mn^{2}-2nm^{2}-\left(-3n^{2}m\right)-\left(-n^{3}\right)$$
- step3: Remove the parentheses:
  $$8m^{3}-12m^{2}n-4mn^{2}-2nm^{2}+3n^{2}m+n^{3}$$
- step4: Subtract the terms:
  $$8m^{3}-14m^{2}n-mn^{2}+n^{3}$$
Expand the expression $$ (2 x-y)(4 x^{2}+2 x y-y^{2}) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(2x-y\right)\left(4x^{2}+2xy-y^{2}\right)$$
- step1: Apply the distributive property:
  $$2x\times 4x^{2}+2x\times 2xy-2xy^{2}-y\times 4x^{2}-y\times 2xy-\left(-y\times y^{2}\right)$$
- step2: Multiply the terms:
  $$8x^{3}+4x^{2}y-2xy^{2}-4yx^{2}-2y^{2}x-\left(-y^{3}\right)$$
- step3: Remove the parentheses:
  $$8x^{3}+4x^{2}y-2xy^{2}-4yx^{2}-2y^{2}x+y^{3}$$
- step4: Subtract the terms:
  $$8x^{3}+0-2xy^{2}-2y^{2}x+y^{3}$$
- step5: Remove 0:
  $$8x^{3}-2xy^{2}-2y^{2}x+y^{3}$$
- step6: Subtract the terms:
  $$8x^{3}-4xy^{2}+y^{3}$$
Here are the expanded forms of the given expressions:

1. For $$ (x-y)(3 x-2 x y+4) $$:
   $$
   3x^{2} - 2x^{2}y + 4x - 3yx + 2y^{2}x - 4y
   $$

2. For $$ (7 m-3 n)(5 m^{2}-2 m n-7 n^{2}) $$:
   $$
   35m^{3} - 29m^{2}n - 43mn^{2} + 21n^{3}
   $$

3. For $$ (2 x-y)(4 x^{2}+2 x y-y^{2}) $$:
   $$
   8x^{3} - 4xy^{2} + y^{3}
   $$

4. For $$ (4 m-n)(2 m^{2}-3 m n-n^{2}) $$:
   $$
   8m^{3} - 14m^{2}n - mn^{2} + n^{3}
   $$

If you need further assistance or additional calculations, feel free to ask!
Here are the expanded forms of the expressions: 1. $$ (x - y)(3x - 2xy + 4) = 3x^2 - 2x^2y + 4x - 3xy + 2y^2x - 4y $$ 2. $$ (7m - 3n)(5m^2 - 2mn - 7n^2) = 35m^3 - 29m^2n - 43mn^2 + 21n^3 $$ 3. $$ (2x - y)(4x^2 + 2xy - y^2) = 8x^3 - 4xy^2 + y^3 $$ 4. $$ (4m - n)(2m^2 - 3mn - n^2) = 8m^3 - 14m^2n - mn^2 + n^3 $$

\( (x-y)(3 x-2 x y+4) \) 5. \( (7 m-3 n)\left(5 m^{2}-2 m n-7 n^{2}\right) \) 7. \( (2 x-y)\left(4 x^{2}+2 x y-y^{2}\right) \) 9. \( (4 m-n)\left(2 m^{2}-3 m n-n^{2}\right) \)

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