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Câu 1:
\(A\left(x\right)+B\left(x\right)\)
\(=\left(6x-4x^3+x-1\right)+\left(-3x-2x^3-5x^2+x+2\right)\)
\(=\left(6x+-3x+x\right)-\left(4x^3+2x^3\right)-5x^2+\left(-1+2\right)\)
\(=-6x^3-5x^2+4x+1\)
\(A\left(x\right)-B\left(x\right)\)
\(=\left(6x-4x^3+x-1\right)-\left(-3x-2x^3-5x^2+x+2\right)\)
\(=\left(-4x^3+2x^3\right)+5x^2+\left(6x+x-x\right)+\left(-1-2\right)\)
\(=-2x^3+5x^2+6x-3\)
\(A+B+C=x^2yz+xy^2z+xyz^2=xyz\left(x+y+z\right)=xyz\)
\(A=x^2yz\) \(B=xy^2z\) \(C=xyz^2\)
\(A+B+C=x^2yz+xy^2z+xyz^2\)
\(=xyz\left(x+y+z\right)=xyz.1=xyz\)
\(3xyz^2+\left(-\frac{4}{8}\right)xyz^5\cdot\frac{1}{3}xyz\)
\(=3xyz^2-\frac{1}{2}xyz\cdot\frac{1}{3}xyz\)
\(=3xyz-\frac{1}{6}x^2y^2z^2\)
\(xyz\left(3-\frac{1}{6}xyz\right)\)
b) \(3xyz^5\cdot\left(-\frac{1}{7}\right)xyz\cdot\frac{-1}{8}xyz^4\)
\(=\left[3\cdot\left(-\frac{1}{7}\right)\cdot\left(-\frac{1}{8}\right)\right]\left(x\cdot x\cdot x\right)\left(y\cdot y\cdot y\right)\left(z^5\cdot z\cdot z^4\right)\)
\(=\frac{3}{56}x^3y^3z^{10}\)
a, \(3xyz^2+\left(\frac{-4}{8}xyz^5\right)\cdot\frac{1}{3}xyz=3xyz^2+\left[\left(\frac{-4}{8}\right)\cdot\frac{1}{3}\right]xyz^5xyz\)\(=3xyz^2-\frac{1}{2}x^2y^2z^6\)
b, \(3xyz^5\cdot\left(\frac{-1}{7}xyz^2\right)\cdot\frac{-1}{8}xyz^4=\left[3\cdot\left(\frac{-1}{7}\right)\cdot\left(\frac{-1}{8}\right)\right]xyz^5xyz^2xyz^4=\frac{3}{56}x^3y^3z^{11}\)
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Ta có:
\(A=x^2yz=x.x.y.z=x.xyz\left(1\right)\)
\(B=xy^2z=x.y.y.z=y.xyz\left(2\right)\)
\(C=xyz^2=x.y.z.z=z.xyz\left(3\right)\)
Lấy (1)+(2)+(3),vế theo vế ta được:
\(A+B+C=x.xyz+y.xyz+z.xyz=\left(x+y+z\right).xyz=xyz\) (vì x+y+z=1)
Vậy A+B+C=xyz (đpcm)
a) Ta có: A+B
\(=xyz-3x^2+5xy-8+5x^2+xyz-5xy-y^2+61\)
\(=2x^2-y^2+2xyz+53\)
b) Ta có: A-B
\(=xyz-3x^2+5xy-8-5x^2-xyz+5xy+y^2-61\)
\(=-8x^2+y^2+10xy-69\)
Theo bài ra,ta có:
\(xyz=-20\cdot\frac{1}{2}\cdot\frac{1}{5}=-\frac{20}{10}=-2\)
\(\Rightarrow A=-2+\left(-2\right)^2+\left(-2\right)^3+.....+\left(-2\right)^{2019}\)
\(\Rightarrow-2A=\left(-2\right)^2+\left(-2\right)^3+\left(-2\right)^4+....+\left(-2\right)^{2020}\)
\(\Rightarrow-3A=-2^{2020}+2\)
\(\Rightarrow A=\frac{-2^{2020}+2}{-3}\)
