Question

thực hiện phép chia

a)\(\left(10x^3y-5x^2y^2-25x^4y^3\right):\left(-5xy\right)\)

b)\(\left[15\left(x-y\right)^5-9\left(x-y\right)^4+12\left(y-x\right)^2\right]:\left(y-x\right)^2\)

c)\(\left(27x^3-y^3\right):\left(3x-y\right)\)

d)\(\left(15x^4+4x^3+11x^2+14x-8\right):\left(5x^2+3x-2\right)\)

Answer 1

a, (10x³y - 5x²y² - 25x⁴y³) : (-5xy)

= -2x² + xy + 5x³y²

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b, [15(x - y)⁵ - 9(x - y)⁴ + 12(y - x)² ] : (y - x)²

= [15(x - y)⁵ - 9(x - y)⁴ + 12(x - y)² ] : (x - y)²

= 15(x - y)³ - 9(x - y)² + 12

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c, (27x³ - y³) : (3x - y)

= (3x - y)(9x² + 3xy + y²) : (3x - y)

= 9x² + 3xy + y²

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d, (15x⁴ + 4x³ + 11x² + 14x - 8) : (5x² + 3x - 2)

= (15x⁴ + 9x³ - 5x³ - 6x² - 3x² + 20x² + 2x + 12x - 8)

= [(15x⁴ + 9x³ - 6x²) - (5x³ + 3x² - 2x) + (20x² + 12x - 8)] : (5x² + 3x - 2)

= [3x²(5x² + 3x - 2) - x(5x³ + 3x - 2) + 4(5x² + 3x - 2)] : (5x² + 3x - 2)

= (5x² + 3x - 2)(3x² - x + 4) : (5x² + 3x - 2)

= 3x² - x +4