(-10x^3+2/5y-1/3z).(-1/2xy)
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\(\left(-10x^3+\frac{2}{5}y-\frac{1}{3}z\right)\left(-\frac{1}{2}xy\right)=5x^4y-\frac{1}{5}xy^2+\frac{1}{6}xyz\)
\(\left(-10x^3+\frac{2}{5}y-\frac{1}{3}z\right)\left(-\frac{1}{2}xy\right)\)
\(=-10x^3\left(-\frac{1}{2}xy\right)+\frac{2}{5}y\cdot\left(-\frac{1}{2}xy\right)-\frac{1}{3}z\left(-\frac{1}{2}xy\right)\)
\(=\left[\left(-10\right)\cdot\left(-\frac{1}{2}\right)\right]x^4y+\left[\frac{2}{5}\cdot\left(-\frac{1}{2}\right)\right]xy^2-\left[\frac{1}{3}\cdot\left(-\frac{1}{2}\right)\right]xyz\)
\(=5x^4y-\frac{1}{5}xy^2+\frac{1}{6}xyz\)
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\(a,-2xy^2\left(x^3y-2x^2y^2+5xy^3\right)\\ =-2x^4y^3+4x^3y^4-10x^2y^5\\ b,\left(-2x\right)\left(x^3-3x^2-x+1\right)\\ =-2x^4+6x^3+2x^2-2x\\ c,\left(-10x^3+\dfrac{2}{5}y-\dfrac{1}{3}z\right)\left(-\dfrac{1}{2}zy\right)\\ =5x^3yz-\dfrac{1}{5}y^2z+\dfrac{1}{6}yz^2\\ d,3x^2\left(2x^3-x+5\right)=6x^5-3x^3+15x^2\\ e,\left(4xy+3y-5x\right)x^2y=4x^3y^2+3x^2y^2-5x^3y\\ f,\left(3x^2y-6xy+9x\right)\left(-\dfrac{4}{3}xy\right)\\ =-4x^3y^2+8x^2y^2-12x^2y\)
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\(=\dfrac{5x^5y^4z}{\dfrac{1}{4}xy^2z}+\dfrac{\dfrac{1}{2}x^4y^2z^3}{\dfrac{1}{4}xy^2z}-\dfrac{2xy^3z^2}{\dfrac{1}{4}xy^2z}\)
=20x^4y^2+2x^3z^2-8yz
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3(x-2)-4(2x+1)-5(2x+3)=50
<=>(3x-6)-(8x+4)-(10x+15)=50
<=>3x-6-8x-4-10x-15=50
<=>(3x-8x-10x)+(-6-4-15)=50
<=>-15x-25=50
<=>-15x=75
<=>x=-5
\(3\frac{1}{2}:\left(4-\frac{1}{3}\left|2x+1\right|\right)=\frac{21}{22}\)
<=>\(4-\frac{1}{3}\left|2x+1\right|=\frac{7}{2}:\frac{21}{22}=\frac{11}{3}\)
<=>\(\frac{1}{3}\left|2x+1\right|=4-\frac{11}{3}=\frac{1}{3}\)
<=>\(\left|2x+1\right|=1\)
<=>2x+1=1 hoặc 2x+1=-1
<=>2x=0 hoặc 2x=-2
<=>x=0 hoặc x=-2
Vậy......................
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Áp dụng t/c dtsbn:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{10x}{20}=\dfrac{3z}{12}=\dfrac{5y}{15}=\dfrac{3y}{9}=\dfrac{2z}{8}=\dfrac{10x+3z-5y}{17}=\dfrac{x+3y-2z}{3}\\ \Rightarrow P=\dfrac{10x+3z-5y}{x+3y-2z}=\dfrac{17}{3}\)
Ta có: \(\left(-10x^3+\dfrac{2}{5}y-\dfrac{1}{3}z\right)\cdot\left(-\dfrac{1}{2}xy\right)\)
\(=10x^3\cdot\dfrac{1}{2}xy-\dfrac{2}{5}y\cdot\dfrac{1}{2}xy+\dfrac{1}{3}\cdot\dfrac{1}{2}xyz\)
\(=5x^4y-\dfrac{1}{5}xy^2+\dfrac{1}{6}xyz\)