a) -2 x^3 cdot(x^2-x+1) b) (4 x^5+3 x)(-2 x-4) c) (x-3)(-2 x+1) cdot 5 x c) (2 x-4)(x-2)-(2 x^2+3 x-1) e) (x-3 x^2+5 x^3) cdot(2 x+3 x^4-7) f) (-3 x+5)(-2 x^2-7)+(6 x-1)(x^2-1)

Chúng ta sẽ giải từng biểu thức một:<br /><br />1. \(-2x^{3}\cdot (x^{2}-x+1)\):<br /> \[<br /> -2x^3 \cdot (x^2 - x + 1) = -2x^3 \cdot x^2 + 2x^3 \cdot x - 2x^3 \cdot 1 = -2x^5 + 2x^4 - 2x^3<br /> \]<br /><br />2. \((4x^{5}+3x)(-2x-4)\):<br /> \[<br /> (4x^5 + 3x)(-2x - 4) = 4x^5 \cdot (-2x) + 4x^5 \cdot (-4) + 3x \cdot (-2x) + 3x \cdot (-4)<br /> \]<br /> \[<br /> = -8x^6 - 16x^5 - 6x^3 - 12x<br /> \]<br /><br />3. \((x-3)(-2x+1)\cdot 5x\):<br /> \[<br /> (x - 3)(-2x + 1) \cdot 5x = (x \cdot (-2x) + x \cdot 1 - 3 \cdot (-2x) - 3 \cdot 1) \cdot 5x<br /> \]<br /> \[<br /> = (-2x^2 + x + 6x - 3) \cdot 5x = (-2x^2 + 7x - 3) \cdot 5x<br /> \]<br /> \[<br /> = -10x^3 + 35x^2 - 15x<br /> \]<br /><br />4. \((x-3x^{2}+5x^{3})-(2x+3x^{2}-7)\):<br /> \[<br /> (x - 3x^2 + 5x^3) - (2x + 3x^2 - 7) = x - 3x^2 + 5x^3 - 2x - 3x^2 + 7<br /> \]<br /> \[<br /> = 5x^3 - 6x^2 - x + 7<br /> \]<br /><br />5. \((-3x+5)(-2x^{2}-7)+(6x-1)(x^{2}-1)\):<br /> \[<br /> (-3x + 5)(-2x^2 - 7) + (6x - 1)(x^2 - 1) = (-3x \cdot (-2x^2) + 5 \cdot (-2x^2)) + (-3x \cdot (-7) + 5 \cdot (-7)) + (6x \cdot x^2 + (-1) \cdot x^2) + (6x \cdot (-1) + (-1) \cdot (-1))<br /> \]<br /> \[<br /> = (6x^3 - 10x^2 + 21x - 35) + (6x^3 - x^2 - 6x + 1)<br /> \]<br /> \[<br /> = 12x^3 - 11x^2 + 15x - 34<br /> \]<br /><br />6. \((2x-4)(x-2)-(2x^{2}+3x-1)\):<br /> \[<br /> (2x - 4)(x - 2) - (2x^2 + 3x - 1) = (2x \cdot x + 2x \cdot (-2) - 4 \cdot x - 4 \cdot (-2)) - (2x^2 + 3x - 1)<br /> \]<br /> \[<br /> = (2x^2 - 4x - 4x + 8) - (2x^2 + 3x - 1) = 2x^2 - 8x + 8 - 2x^2 - 3x + 1<br /> \]<br /> \[<br /> = -11x + 9<br /> \]<br /><br />Tóm lại, các kết quả là:<br />1. \(-2x^5 + 2x^4 - 2x^3\)<br />2. \(-8x^6 - 16x^5 - 6x^3 - 12x\)<br />3. \(-10x^3 + 35x^2 - 15x\)<br />4. \(5x^3 - 6x^2 - x + 7\)<br />5. \(12x^3 - 11x^2 + 15x - 34\)<br />6. \(-11x + 9\)