Tính:

a) \({\left( {3x + 1} \right)^2}\)                                  b) \({\left( {4x + 5y} \right)^2}\)                    c) \({\left( {5x - \dfrac{1}{2}} \right)^2}\)                      d) \({\left( { - x + 2{y^2}} \right)^2}\)

Thực hiện phép tính:
a) \(\dfrac{2}{5}xy\left(x^2y-5x+10y\right)\)
b) \(\left(x^2-1\right)\left(x^2+2x+y\right)\)
c) \(\left(x+3y\right)^2\)
d) \(\left(4x-y\right)^3\)
e) \(\left(x^2-2y\right)\left(x^2+2y\right)\)
g) \(18x^4y^2z:10x^4y\)
h) \(\left(x^3y^3+\dfrac{1}{2}x^2y^3-x^3y^2\right):\dfrac{1}{3}x^2y^2\)
i) \(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\)
k) \(\dfrac{5x-1}{3x^2y}+\dfrac{x+1}{3x^2y}\)
l) \(\dfrac{3x+1}{x^2-3x+1}+\dfrac{x^2-6x}{x^2-3x+1}\)
m) \(\dfrac{2x+3}{10x-4}+\dfrac{5-3x}{4-10x}\)
n) \(\dfrac{x}{x^2+2x+1}+\dfrac{3}{5x^2-5}\)
o) \(\dfrac{x^2+2}{x^3-1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
p) \(\dfrac{4x+2}{15x^3y}\dfrac{5y-3}{9x^2y}+\dfrac{x+1}{5xy^3}\)
q) \(\dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\)
r) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
x) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)\)
y) \(\dfrac{x^2-4}{3x+12}.\dfrac{x+4}{2x-4}\)
z) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}\)
t) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
w) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)

Thực hiện các phép tính :

a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)

b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)

c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)

d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)

e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)

Bài 1. tính giá trị biểu thức.

a. \(5x\left(4x^2-2x+1\right)-2x\left(10x^2-5x+2\right)\) với x = 15

b.\(5x\left(x-4y\right)-4y\left(y-5x\right)\) tại \(x=\dfrac{-1}{5}\) và \(y=\dfrac{-1}{2}\)

c.\(6xy\left(xy-y^2\right)-8x^2\left(x-y^2\right)+5y^2\left(x^2-xy\right)\)với \(x=\dfrac{1}{2};y=2\)

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Thực hiện phép tính:

a) \(\dfrac{x+2y}{xy}\div\dfrac{x^2+4xy+4y^2}{2x^2}\)

b) \(\dfrac{4x^3-xy^2}{x^2+xy+y^2}\div\dfrac{\left(2x-y\right)^3}{x^3-y^3}\)

c) \(\dfrac{x+3}{x+2}\div\dfrac{3x+9}{2x-1}\div\dfrac{4x-2}{2x+4}\)

d) \(\dfrac{x+1}{x+2}\div\left(\dfrac{2x^2}{2x-3}\times\dfrac{3x+3}{4x^3}\right)\)

Rút gọn rồi tính giá trị của các biểu thức sau:

a) \(A=2x\left(x-y\right)-y\left(y-2x\right)\) với \(x=-\dfrac{2}{3};y=-\dfrac{1}{3}\)

b)\(B=5x\left(x-4y\right)-4y\:\left(y-5x\right)\) với \(x=-\dfrac{1}{5};y=-\dfrac{1}{2}\)

c)\(C=x\left(x^2+6x\right)+4\left(3x+2\right)\) với \(x=-11\)

d) \(D=5x\left(4x^2-2x+1\right)-2\left(10x^2-5x-2\right)\) với x = 5

e) \(E=\left(y^3+x^2y\right)\left(x^2+y^2\right)-y\left(x^4+y^4\right)\) với x = 1,5 ; y= -2

g) \(G=\left(x^2-x+3\right)\left(-2x^2+3x+5\right)\) với \(\)\(\)giá trị tuyệt đối của x = 2

Rút gọn các biểu thức sau:

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

b/\(\left(4x-y\right)\left(4x+y\right)-2\left(3x-2y\right)^2+\left(x-3y\right)^2\)

c/\(\left(2a-3b+4c\right)\left(2a-3b-4c\right)\)

d/\(\left(3a-1\right)^2+2\left(9a^2-1\right)\left(3a+1\right)\)

e/\(\left(3x-4\right)^2+\left(4-x\right)^2-2\left(3x-4\right)\left(x-4\right)\) 

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Rút gọn các phân thức :

a, \(\dfrac{x^{2^{ }}-4}{2x^{2^{ }}-4x}\)

b, \(\dfrac{2x-x^2}{x^2-4x+4}\)

c, \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

d, \(\dfrac{5x^2+10x+5}{x+x^2}\)

e, \(\dfrac{3x^2+3x}{\left(x+1\right) \left(2x+6\right)}\)

f, \(\dfrac{\left(2-3x\right)\left(x+1\right)}{x^2+2x+1}\)