Question

Bài 1: rút gọn các biểu thức sau:

a, (5x -10) (1/2 x^2 - 3x + 2/5) + (x -2) (1/5 x^2 + 15x - 2)

b, (-2x^2 + 6x) (3x - 1) + (6x -2) (x^2 - 3x + 3)

Answer 1

a, \(=\dfrac{5}{2}x^3-15x^2+2x-5x^2+30x-4+\dfrac{1}{5}x^3+15x^2-2x-\dfrac{2}{5}x^2-30x+4=\dfrac{27}{10}x^3-\dfrac{27}{5}x^2\)

b, \(=-6x^3+2x^2+18x^2-6x+6x^3-18x^2+18x-2x^2+6x-6=18x-6\)

Answer 2

a: \(\left(5x-10\right)\left(\dfrac{1}{2}x^2-3x+5\right)+\left(x-2\right)\left(\dfrac{1}{5}x^2+15x-2\right)\)

\(=\left(x-2\right)\left(\dfrac{5}{2}x^2-15x+25\right)+\left(x-2\right)\left(\dfrac{1}{5}x^2+15x-2\right)\)

\(=\left(x-2\right)\left(\dfrac{5}{2}x^2-15x+25+\dfrac{1}{5}x^2+15x-2\right)\)

\(=\left(x-2\right)\left(\dfrac{27}{10}x^2+23\right)=\dfrac{27}{10}x^3+23x-\dfrac{27}{5}x^2-46\)

b: \(\left(-2x^2+6x\right)\left(3x-1\right)+\left(6x-2\right)\left(x^2-3x+3\right)\)

\(=-6x^3+2x^2+18x^2-6x+6x^3-18x^2+18x-2x^2+6x-6\)

\(=-6+18x\)