. (5,7x^2y - 3,1xy + 8y^3) - (6,9xy - 2,3x^2y - 8y^3)
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a) \(\left(3x+y-z\right)-\left(4x-2y+6z\right)\)
\(=3x+y-z-4x+2y-6z\)
\(=-x+3y-7z\)
b) \(\left(x^3+6x^2+5y^3\right)-\left(2x^3-5x+7y^3\right)\)
\(=x^3+6x^2+5y^3-2x^3+5x-7y^3\)
\(=-x^3+6x^2+5x-2y^3\)
c) \(\left(5,7x^{2y}-3,1xy+8y^3\right)-\left(6,9xy-2,3x^{2y}-8y^3\right)\)
\(=5,7x^{2y}-3,1xy+8y^3-6,9xy+2,3x^{2y}+8y^3\)
\(=8x^{2y}-10xy+16y^3\)
\(\left(\dfrac{x}{x+2y}-\dfrac{x+2y}{2y}\right)\left(\dfrac{x}{x-2y}-1+\dfrac{8y^3}{8y^3-x^3}\right)=\dfrac{2xy-\left(x+2y\right)^2}{2y\left(x+2y\right)}\left(\dfrac{2y}{x-2y}+\dfrac{8y^3}{\left(2y-x\right)\left(4y^2+2yx+x^2\right)}\right)=\dfrac{-\left(x^2+2xy+4y^2\right)}{2y\left(x+2y\right)}\cdot\dfrac{2y\left(4y^2+2yx+x^2\right)-8y^3}{\left(x-2y\right)\left(x^2+2xy+4y^2\right)}=\dfrac{-\left(x^2+2xy+4y^2\right)2y\left(4y^2+2xy+x^2-4y^2\right)}{2y\left(x+2y\right)\left(x-2y\right)\left(x^2+2x+4y^2\right)}=\dfrac{-\left(x^2+2xy\right)}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{x}{2y-x}\)
a: \(=3x+y-z-4x+2y-6z=-x+3y-7z\)
b: \(=x^3+6x^2+5y^3-2x^3+5x-7y^3=-x^3+6x^2+5x-2y^3\)
c: \(=5.7x^2y-3.1xy+8y^3-6.9xy+2.3x^2y+8y^3\)
\(=8x^2y-10xy+16y^3\)
2(2y + 1)(8y - 3) + (3 - 4y)(8y - 7) = 6y + 73
32y2 - 12y + 16y - 6 + 24y - 21 - 32y2 + 28y = 6y + 73
56y - 27 = 6y + 73
56y - 6y = 73 + 27
50y = 100
y = 100 : 50
y = 2
2(2y + 1)(8y - 3) + (3 - 4y)(8y - 7) = 6y + 73
32y2 - 12y + 16y - 6 + 24y - 21 - 32y2 + 28y = 6y + 73
56y - 27 = 6y + 73
56y - 6y = 73 + 27
50y = 100
y = 100 : 50
y = 2
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