(5x-c)(x-5c) (4m+3n)(4m+3n) (3y-2v)(3y+2v) (10x+3z)(10x-5z)

To simplify or expand the given expressions, we will use the distributive property (also known as the FOIL method for binomials). Here are the expanded forms for each expression:

1. \((5x - c)(x - 5c)\): \[ = 5x \cdot x + 5x \cdot (-5c) - c \cdot x - c \cdot (-5c) \] \[ = 5x^2 - 25xc - cx + 5c^2 \] \[ = 5x^2 - 26xc + 5c^2 \]

2. \((4m + 3n)(4m + 3n)\): This is a perfect square: \[ = (4m + 3n)^2 \] \[ = (4m)^2 + 2(4m)(3n) + (3n)^2 \] \[ = 16m^2 + 24mn + 9n^2 \]

3. \((3y - 2v)(3y + 2v)\): This is a difference of squares: \[ = (3y)^2 - (2v)^2 \] \[ = 9y^2 - 4v^2 \]

4. \((10x + 3z)(10x - 5z)\): This is also a difference of squares: \[ = (10x)^2 - (5z)^2 \] \[ = 100x^2 - 25z^2 \]

To summarize the expansions:

1. \(5x^2 - 26xc + 5c^2\)
2. \(16m^2 + 24mn + 9n^2\)
3. \(9y^2 - 4v^2\)
4. \(100x^2 - 25z^2\)