1.Với giá trị nào của biến thì giá trị của biểu thức bằng 0

\(\frac{x+1}{7};\frac{3x+3}{5};\frac{3x\left(x-5\right)}{x-7};\frac{2x\left(x+1\right)}{3x+4}\)

2.Tính giá trị của các biểu thức sau:

\(A=\frac{a^2\left(a^2+b^2\right)\left(a^{\text{4}}+b^{\text{4 }}\right)\left(a^8+b^8\right)\left(a^2-3b\right)}{\left(a^{10}+b^{10}\right)}\)tại a=6;b=12

\(B=3xy\left(x+y\right)+2x^3y+2x^2y^2+5\)tại x+y=0

\(C=2x+2y+3xy\left(x+y\right)+5\left(x^3y^2+x^2y^3\right)+4\)tại x+y=0

Giải hệ phương trình
\(\left\{{}\begin{matrix}4\left(2x-y+3\right)-3\left(x-2y+3\right)=48\\3\left(3x-4y+3\right)+4\left(4x-2y-9\right)=48\end{matrix}\right.\)

\(\left\{{}\begin{matrix}6\left(x+y\right)=8+2x-3y\\5\left(y-x\right)=5+3x+2y\end{matrix}\right.\)

\(\left\{{}\begin{matrix}-2\left(2x+1\right)+1,5=3\left(y-2\right)-6x\\11,5-4\left(3-x\right)=2y-\left(5-x\right)\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{8x-5y-3}{7}+\dfrac{11y-4x-7}{5}=12\\\dfrac{9x+4y-13}{5}-\dfrac{3\left(x-2\right)}{4}=15\end{matrix}\right.\)

\(\left\{{}\begin{matrix}2\sqrt{3}x-\sqrt{5}y=2\sqrt{6}-\sqrt{15}\\3x-y=3\sqrt{2}-\sqrt{3}\end{matrix}\right.\)

1. tính

a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)

b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)

c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)

d) \(\left(\dfrac{1}{2}x-2y\right)^3\)

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

f) \(27x^3-8y^3\)

g) 4(2x - 3y) - 4 - (2x-3y)²

2. rút gọn

a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)

b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)

c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)

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

3. c/m các biểu thức sau ko phụ thuộc vào biến x,y

a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)

b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)

c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)

d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)

4. Tìm x

a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)

b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)

c) \(49x^2+14x+1=0\)

d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)

5. c/m biểu thức luôn dương:

a) \(A=16x^2+8x+3\)

b) \(B=y^2-5y+8\)

c) C= \(2x^2-2x+2\)

d) \(D=9x^2-6x+25y^2+10y+4\)

6. Tìm GTLN và GTNN của các biểu thức sau

a) \(M=x^2+6x-1\)

b) \(N=10y-5y^2-3\)

7. thu gọn

a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)

b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)

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

BT10: Thực hiện phép tính

\(a,-xyz^2\)\(-3xz.yz\)

\(b,-8x^2\)\(y-x.\left(xy\right)\)

\(c,4xy^2\) \(.x-\left(-12x^2y^2\right)\)

\(d,\dfrac{1}{2}x^2y^3-\dfrac{1}{3}x^2y.y^2\)

\(e,3xy\left(x^2y\right)-\dfrac{5}{6}x^3y^2\)

\(f,\dfrac{3}{4}x^4y-\dfrac{1}{6}xy.x^3\)

giải hệ phương trình

1, \(\left\{{}\begin{matrix}2x^2+3y=17\\3x^2-2y=6\end{matrix}\right.\)

2, \(\left\{{}\begin{matrix}\left|x-1\right|+\left|y-1\right|=2\\4\left|x-1\right|+3\left|y-1\right|=7\end{matrix}\right.\)

3, \(\left\{{}\begin{matrix}3\sqrt{x-1}+2\sqrt{y}=2\\2\sqrt{x-1}-\sqrt{y}=4\end{matrix}\right.\)

4 , \(\left\{{}\begin{matrix}x+y=2\\\left|2x-3y\right|=1\end{matrix}\right.\)

5 , \(\left\{{}\begin{matrix}2x-y=1\\\left|x-y\right|=\left|2y-1\right|\end{matrix}\right.\)

6,\(\left\{{}\begin{matrix}\left(x-3\right)\left(y+6\right)=xy\\\left(x+2\right)\left(y-2\right)=xy\end{matrix}\right.\)

7 , \(\left\{{}\begin{matrix}\left(x-3\right)\left(2y+5\right)=\left(2x+7\right)\left(y-1\right)\\\left(4x+1\right)\left(3y-6\right)=\left(6x-1\right)\left(2y+3\right)\end{matrix}\right.\)

8 , \(\left\{{}\begin{matrix}4x^2-5\left(y+1\right)=\left(2x-3\right)^2\\3\left(7x+2\right)=5\left(2y-1\right)-3x\end{matrix}\right.\)