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NH
1
H
5 tháng 10 2023
\(A,xy\left(2x^2-3\right)-x^2\left(5xy+y\right)+x^2y\\ =2x^3y-3xy-5x^3y-x^2y+x^2y\\ =\left(2x^3y-5x^3y\right)+\left(-x^2y+x^2y\right)-3xy\\ =-3x^3y-3xy\)
\(B,3xyz\left(y-2\right)-5yz\left(1-y\right)-8z\left(y^2-3\right)\\ =3xy^2z-6xyz-5yz+5y^2z-8y^2z+24z\\ =3xy^2z-6xyz+\left(5y^2z-8y^2z\right)-5yz+24z\\ =3xy^2z-6xyz-3y^2z-5yz+24z\)
10 tháng 8 2019
\(A=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x-2\right)\left(x^2+2x+4\right).\)
\(=x^3+y^3-\left(x^3-8\right)\)
\(=y^3+8\)
17 tháng 4 2021
Ta có: \(\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{x^3-y^3}-2+\dfrac{y}{y-x}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{2\left(x^3-y^3\right)-y\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\dfrac{2x^3+x^2y-xy^2-2x^3+2y^3-x^2y-xy^2-y^3}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}-\dfrac{y^3-2xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{y^2\left(x-y\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\cdot\dfrac{x}{x-y}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x^2-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x^3-xy^2+xy^2-x^3-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
YN
1 tháng 7 2021
\(a)\)
\(\left(2x+3\right)^2+\left(2x-3\right)^2-\left(2x+3\right)\left(4x-6\right)+xy\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x-3\right)+\left(2x-3\right)^2+xy\)
\(=\left(2x+3-2x+3\right)^2+xy\)
\(=6^2+2\left(-1\right)\)
\(=36-2\)
\(=34\)
\(b)\)
\(\left(x-2\right)^2-\left(x-1\right)\left(x+1\right)-x\left(1-x\right)\)
\(=x^2-4x+4-x^2+1-x+x^2\)
\(=x^2-5x+5\)
Thay \(x=-2\)vào ta có:
\(\left(-2\right)^2-5\left(-2\right)+5\)
\(=4+10+5\)
\(=19\)
12 tháng 10 2021
\(P=x^2+8x+16+x^2-25-2x^2-2x=6x-9\\ Q=y\left(x-4\right)-5\left(x-4\right)=\left(y-5\right)\left(x-4\right)\\ Q=\left(5,5-5\right)\left(14-4\right)=0,5\cdot10=5\)
\(\frac{xy+2x-y-2}{xy-x-y+1}=\frac{\left(xy-y\right)+\left(2x-2\right)}{\left(xy-y\right)+\left(1-x\right)}\)
\(=\frac{\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y-1\right)}=\frac{y+2}{y-1}\)
\(\frac{\left(xy-y\right)+\left(2x-2\right)}{\left(xy-y\right)-\left(x-1\right)}=\frac{y\left(x-1\right)+2\left(x-1\right)}{y\left(x-1\right)-\left(x-1\right)}=\frac{\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y-1\right)}=\frac{y+2}{y-1}\)