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1. 20\(x^2y^3\) : 4x\(y^2\) = 5xy
2. \(\dfrac{-1}{2}x^4y^4\) : \(\dfrac{2}{3}x^2y^2\) = \(\dfrac{-3}{4}x^2y^2\)
3. \(\left(-xy\right)^6:\left(-xy\right)^2=\left(-xy\right)^2\) = xy
4. 27\(x^2y^3z^4:\left(-3xyz\right)^2\) = 27\(x^2y^3z^4\) : 9 \(x^2y^2z^2\) = 3y\(z^2\)
5. \(\left(-x\right)^{10}:\left(-x\right)^5=\left(-x\right)^2\) = x
1,\(\dfrac{x^2-6x+9}{x^2-8x+15}=\dfrac{\left(x-3\right)^2}{\left(x-3\right).\left(x-5\right)}=\dfrac{x-3}{x-5}\)
2,\(\dfrac{x^2+5x}{2x+10}=\dfrac{x.\left(x+5\right)}{2.\left(x+5\right)}=\dfrac{x}{2}\)
3,\(\dfrac{25-10x+x^2}{xy-5y}=\dfrac{\left(x-5\right)^2}{y.\left(x-5\right)}=\dfrac{x-5}{y}\)
4,\(\dfrac{x^2+3x-y^2-3y}{x^2-y^2}\\ \\ =\dfrac{\left(x+y\right).\left(x-y\right)+3.\left(x-y\right)}{\left(x-y\right).\left(x+y\right)}\\ \\ =\dfrac{\left(x-y\right).\left(x+y+3\right)}{\left(x-y\right).\left(x+y\right)}\\ \\ =\dfrac{x+y+3}{x+y}\)5,\(\dfrac{x^3+2x^2-x-2}{x^3-3x+2}=\dfrac{x^2.\left(x+2\right)-\left(x+2\right)}{x.\left(x^2-1\right)-2.\left(x-1\right)}\\ \\ \dfrac{\left(x+2\right).\left(x^2-1\right)}{x.\left(x+1\right).\left(x-1\right)-2.\left(x-1\right)}\\ =\dfrac{\left(x+2\right).\left(x+1\right).\left(x-1\right)}{\left(x-1\right).\left[\left(x+1\right).x-2\right]}=\dfrac{\left(x+2\right).\left(x+1\right)}{\left(x+1\right).x-2}\)
a: \(25x^2-\dfrac{10}{3}xy+\dfrac{1}{9}y^2=\left(5x-\dfrac{1}{3}y\right)^2\)
b: \(25x^2-15x+\dfrac{9}{4}=\left(5x-\dfrac{3}{2}\right)^2\)
c: \(\left(2x+\dfrac{1}{2}y\right)\left(4x^2-xy+\dfrac{1}{4}y^2\right)=8x^3+\dfrac{1}{8}y^3\)
d: \(\left(x^2-\dfrac{2}{3}\right)\left(x^4+\dfrac{2}{3}x^2+\dfrac{4}{9}\right)=x^6-\dfrac{8}{27}\)
A=26x2+y(2x+y)-10x(x+y)
A=26x2+2xy+y2-10x2-10xy
A=16x2-8xy+y2 =(4x)2-2.4x.y+y2 =(4x-y)2
Thay x=0,25y,ta có: A=(4.0,25y - y)2=(y-y)2=0
B=x3+6x2y+12xy2+8y3
B=x3+3x22y+3x(2y)2+(2y)3 =(x+2y)3
Có x+2y=-5 ⇒ x=-5-2y
Thay x=-5-2y vào, ta có B=(-5-2y+2y)3=(-5)3=-125
1: \(=\dfrac{x\left(x-1\right)-y\left(x-1\right)}{x\left(y-1\right)-y\left(y-1\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x-y\right)\left(y-1\right)}=\dfrac{x-1}{y-1}\)
2: \(=\dfrac{\left(x-2\right)^2}{\left(x+5\right)\left(x-2\right)}=\dfrac{x-2}{x+5}\)
3: \(=\dfrac{\left(x-2y\right)^2}{y\left(x-2y\right)}=\dfrac{x-2y}{y}\)
4: \(=\dfrac{x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}=\dfrac{1}{x+3}\)
5: \(=\dfrac{x\left(x-y\right)}{3\left(x-y\right)\left(x+y\right)}=\dfrac{x}{3\left(x+y\right)}\)
1: \(=\dfrac{x\left(x-1\right)-y\left(x-1\right)}{x\left(y-1\right)-y\left(y-1\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x-y\right)\left(y-1\right)}=\dfrac{x-1}{y-1}\)
2: \(=\dfrac{\left(x-2\right)^2}{\left(x+5\right)\left(x-2\right)}=\dfrac{x-2}{x+5}\)
3: \(=\dfrac{\left(x-2y\right)^2}{y\left(x-2y\right)}=\dfrac{x-2y}{y}\)
4: \(=\dfrac{x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}=\dfrac{1}{x+3}\)
5: \(=\dfrac{x\left(x-y\right)}{3\left(x-y\right)\left(x+y\right)}=\dfrac{x}{3\left(x+y\right)}\)
a: \(=\dfrac{5x^2y^4}{-10x^2y}=-\dfrac{1}{2}y^3=-\dfrac{1}{2}\cdot8=-4\)
b: \(=\dfrac{15x^4y^2}{5x^3y}+\dfrac{20x^3y^2}{5x^2y}=3xy+4xy=7xy\)
\(=7\cdot\dfrac{1}{7}\cdot2009=2009\)
a: Ta có: \(\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)+1\)
\(=\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1\)
\(=\left(x^2+9x\right)^2+38\left(x^2+9x\right)+360+1\)
\(=\left(x^2+9x\right)^2+2\cdot\left(x^2+9x\right)\cdot19+19^2\)
\(=\left(x^2+9x+19\right)^2\)
b. \(x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)
\(=\left(x^2+2x+1\right)+2\left(x+1\right)\left(y+1\right)+\left(y^2+2y+1\right)\)
\(=\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\)
\(=\left(x+1+y+1\right)^2=\left(x+y+2\right)^2\)
c. \(x^2-2x\left(y+2\right)+y^2+4y+4\)
\(=x^2-2x\left(y+2\right)+\left(y+2\right)^2\)
\(=\left(x-y-2\right)^2\)
d. \(x^2+2x\left(y+1\right)+y^2+2y+1\)
\(=x^2+2x\left(y+1\right)+\left(y+1\right)^2\)
\(=\left(x+y+1\right)^2\)
x3*[x+y2 ]*[x2-y3]*[x2-y]:[x2+y2+1]
thay x=3;y=9 ta đc
33*[3+92]*[32-92]*[32-9]:[32+92+1]
=33*[3+92]*[32-92]*[9-9]:[32+92+1]
=33*[3+92]*[32-92]*0:[32+92+1]
=0:[32+92+1]
=0
1: \(=\dfrac{x^2-1}{x\left(x^2-1\right)}=\dfrac{1}{x}\)
2: \(=\dfrac{\left(x-2\right)\left(x+2\right)}{y\left(x-2\right)}=\dfrac{x+2}{y}\)
3: \(=\dfrac{2x^2+2xy-xy-y^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{\left(x+y\right)\left(2x-y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{2x-y}{x-y}\)
4: \(=\dfrac{x\left(x^2-1\right)}{x\left(x^2-x-2\right)}=\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}=\dfrac{x-1}{x-2}\)