Expand and simplify: \( \begin{array}{lllll}\text { (1) } 3 x(x+3) & \text { (2) } & -3 a\left(3 a^{3}-6 a^{2}+a\right) & \text { (3) } & (x+5)(x+2) \\ \text { (4) }(x-5)(x-2) & \text { (5) } & (x+5)(x-2) & \text { (4) } & (x-5)(x+2) \\ \text { (7) }(3 x-1)(2 x+3) & \text { (8) } & (7 m-2 n)(3 m+4 n) \\ \text { (9) }\left(2 x^{4}-3 y^{2}\right)\left(3 x^{4}+2 y^{2}\right) & \text { (10) }\left(4 x^{4}+3 y^{5}\right)\left(2 x^{4}-4 y^{3}\right)\end{array} \)

Let's tackle each expression one by one! (1) For \( 3x(x+3) \), we distribute \( 3x \): \[ 3x \cdot x + 3x \cdot 3 = 3x^2 + 9x. \] (2) For \( -3a(3a^3 - 6a^2 + a) \), distribute \(-3a\): \[ -3a \cdot 3a^3 + (-3a) \cdot (-6a^2) + (-3a) \cdot a = -9a^4 + 18a^3 - 3a^2. \] (3) Expanding \( (x+5)(x+2) \): \[ x \cdot x + x \cdot 2 + 5 \cdot x + 5 \cdot 2 = x^2 + 2x + 5x + 10 = x^2 + 7x + 10. \] (4) Expanding \( (x-5)(x-2) \): \[ x \cdot x + (-5) \cdot x + (-2) \cdot x + (-5)(-2) = x^2 - 2x - 5x + 10 = x^2 - 7x + 10. \] (5) Expanding \( (x+5)(x-2) \): \[ x \cdot x + (-2) \cdot x + 5 \cdot x + 5 \cdot (-2) = x^2 - 2x + 5x - 10 = x^2 + 3x - 10. \] (6) Expanding \( (x-5)(x+2) \): \[ x \cdot x + 2 \cdot x + (-5) \cdot x + (-5) \cdot 2 = x^2 + 2x - 5x - 10 = x^2 - 3x - 10. \] (7) Expanding \( (3x-1)(2x+3) \): \[ 3x \cdot 2x + 3x \cdot 3 + (-1) \cdot 2x + (-1) \cdot 3 = 6x^2 + 9x - 2x - 3 = 6x^2 + 7x - 3. \] (8) Expanding \( (7m-2n)(3m+4n) \): \[ 7m \cdot 3m + 7m \cdot 4n + (-2n) \cdot 3m + (-2n) \cdot 4n = 21m^2 + 28mn - 6mn - 8n^2 = 21m^2 + 22mn - 8n^2. \] (9) Expanding \( (2x^4 - 3y^2)(3x^4 + 2y^2) \): \[ 2x^4 \cdot 3x^4 + 2x^4 \cdot 2y^2 - 3y^2 \cdot 3x^4 - 3y^2 \cdot 2y^2 = 6x^8 + 4x^4y^2 - 9x^4y^2 - 6y^4 = 6x^8 - 5x^4y^2 - 6y^4. \] (10) Expanding \( (4x^4 + 3y^5)(2x^4 - 4y^3) \): \[ 4x^4 \cdot 2x^4 + 4x^4 \cdot (-4y^3) + 3y^5 \cdot 2x^4 + 3y^5 \cdot (-4y^3) = 8x^8 - 16x^4y^3 + 6x^4y^5 - 12y^8 = 8x^8 - 16x^4y^3 + 6x^4y^5 - 12y^8. \] These expansions cover all the expressions provided!