Realiza las siguientes operaciones : a) \( 3 \cdot\left(2 x^{2}-4 x+5\right)-\left(6 x^{2}-12 x+15\right)= \) b) \( 2 \cdot\left(2 x^{3}-3 x+4\right)-3 \cdot\left(x^{3}-2 x^{2}+x-1\right)= \) c) \( 4 \cdot\left(x^{3}-2 x\right)-2 \cdot\left(x-x^{3}\right)= \) d) \( -2 \cdot(-3 x+4)-(5 x+8)= \) e) \( x-8-5 x-8= \) f) \( -(9 x-4)+5 \cdot(3 x-2)= \) g) \( 5 x+3 y-2 \cdot(x+6 y)+3 \cdot(2 x-8)= \) h) \( -(8 x-5 x+4)-4 \cdot(4 x-1)= \) i) \( 5 \cdot\left(x^{2}-3 x+1\right)-\left(2 x^{2}+5 x+3\right)= \) j) \( -\left(x^{2}-3 x\right)+x^{3}-2 x^{2}+x-4 \cdot\left(x^{2}-5 x\right)= \) k) \( \left(4 x^{2}-2 x+1\right) \cdot\left(x^{2}-2\right)= \) l) \( \left(-3 x^{3}+6 x^{2}-x-4\right) \cdot\left(3 x^{2}-5 x\right)= \)

Claro, a continuación se realizan y simplifican las operaciones solicitadas: **a)** \[ 3 \cdot (2x^{2} - 4x + 5) - (6x^{2} - 12x + 15) = 0 \] **b)** \[ 2 \cdot (2x^{3} - 3x + 4) - 3 \cdot (x^{3} - 2x^{2} + x - 1) = x^{3} + 6x^{2} - 9x + 11 \] **c)** \[ 4 \cdot (x^{3} - 2x) - 2 \cdot (x - x^{3}) = 6x^{3} - 10x \] **d)** \[ -2 \cdot (-3x + 4) - (5x + 8) = x - 16 \] **e)** \[ x - 8 - 5x - 8 = -4x - 16 \] **f)** \[ -(9x - 4) + 5 \cdot (3x - 2) = 6x - 6 \] **g)** \[ 5x + 3y - 2 \cdot (x + 6y) + 3 \cdot (2x - 8) = 9x - 9y - 24 \] **h)** \[ -(8x - 5x + 4) - 4 \cdot (4x - 1) = -19x \] **i)** \[ 5 \cdot (x^{2} - 3x + 1) - (2x^{2} + 5x + 3) = 3x^{2} - 20x + 2 \] **j)** \[ -(x^{2} - 3x) + x^{3} - 2x^{2} + x - 4 \cdot (x^{2} - 5x) = x^{3} - 7x^{2} + 24x \] **k)** \[ (4x^{2} - 2x + 1) \cdot (x^{2} - 2) = 4x^{4} - 2x^{3} - 7x^{2} + 4x - 2 \] **l)** \[ (-3x^{3} + 6x^{2} - x - 4) \cdot (3x^{2} - 5x) = -9x^{5} + 33x^{4} - 33x^{3} - 7x^{2} + 20x \]