Question

Thực hiện phép tính (các bạn ơi giúp mình nhé :((( mai mình thi rồi)

1/ 4x² . (5x³ + 2x - 1)

2/ 4x³y² : x²

3/ (15x²y³ - 10x³y³ + 6xy) : 5xy

4/ (5x³ + 14x² + 12x + 8) : (x + 2)

5/ 7/2x + 11/3y²

6/ x/x+2 + 3/(x+2)(4x-7)

7/ 3/x-y - 2x²/x+y

8/ (1/2) x²y² . (2x+y) (2x-y)

9/ (x-1/2) (x+1/2) (4x-1)

10/ 3x/2x+6 + 6-x/2x²+6x

11/ x²-1/2x-2 + 3x+3/1-x²

12/ x²/x²-y² - xy/x²-y²

13/ 2/2x-3 + x/x-1 - 5x+3/2x²+3-5x

15/ (x-y) (x²+xy+y²) + 2y³ : y³

Answer 1

1) 4x\(^2\).(5x³+2x-1)

= 20x\(^5\)+8x\(^3\)-4x\(^2\).

2) 4x\(^3\): x²

= 4x

3) ( 15x²y³-10x³y³+6xy): 5xy

= 3xy²-2x²y²+\(\dfrac{6}{5}\)

4) (5x³+14x²+12x+8 ): (x+2)

= 5x²+4x+4

5)\(\dfrac{7}{2x}\)+\(\dfrac{11}{3y^2}\)

=\(\dfrac{7.3y^2+11.2x}{6xy^2}\) =\(\dfrac{21y^2+22x}{6xy^2}\) = \(\dfrac{21+22}{6}\) =\(\dfrac{43}{6}\)

6) \(\dfrac{x}{x+2}\) +\(\dfrac{3}{\left(x+2\right)\left(4x-7\right)}\)

7)\(\dfrac{3}{x-y}\)-\(\dfrac{2x^2}{x+y}\)

= \(\dfrac{3\left(x+y\right)-2\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}\)=\(\dfrac{3x+3y-2x-2y}{\left(x-y\right)\left(x+y\right)}\)=\(\dfrac{x+y}{\left(x-y\right)\left(x+y\right)}\)=\(\dfrac{1}{x-y}\).

8)\(\dfrac{1}{2}\)x²y².(2x+y)(2x-y)

= \(\dfrac{1}{2}\)x²y².(4x²-2xy+2xy-y²)

= \(\dfrac{1}{2}\)x²y².(4x²-y²)

= 2x⁴y²-\(\dfrac{1}{2}\)x²y⁴

9) (x-\(\dfrac{1}{2}\)).(x+\(\dfrac{1}{2}\)).(4x-1)

= x².(4x-1)

= 4x³-x²

10)\(\dfrac{3x}{2x+6}\)+\(\dfrac{6-x}{2x^2+6x}\)

= \(\dfrac{3x}{2\left(x+3\right)}\)+\(\dfrac{6-x}{2x\left(x+3\right)}\)= \(\dfrac{3x^2+6-x}{2x\left(x+3\right)}\)=\(\dfrac{3-x}{3}\)= -x

11) x²-\(\dfrac{1}{2x-2}\)+3x+\(\dfrac{3}{1-x^2}\)

12)\(\dfrac{x^2}{x^2-y^2}\)-\(\dfrac{x-y}{x^2-y^2}\)

= \(\dfrac{x^2-xy}{\left(x-y\right)\left(x+y\right)}\)=\(\dfrac{x\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\)= \(\dfrac{x}{x+y}\)