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a) \(x\left(xy+1\right)+y\left(xy-1\right)-xy\left(x+y\right)\)
\(=X^2y+x+xy^2-y-x^2y-xy^2\)
\(=x-y\)
a.
\(\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)-x^4+y^4=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4-x^4+y^4\)
\(=\left(x^4-x^4\right)+\left(y^4-y^4\right)+\left(x^3y-x^3y\right)+\left(xy^3-xy^3\right)+\left(x^2y^2-x^2y^2\right)=0\)
b.
\(\left(2-x\right)\left(1+2x\right)+\left(1+x\right)-\left(x^4+x^3-5x^2-5\right)=2+4x-x-2x^2+1+x-x^4-x^3+5x^2+5\)
\(=-x^4-x^3+\left(5x^2-2x^2\right)+\left(4x-x+x\right)+\left(1+2+5\right)=-x^4-x^3+3x^2+4x+8\)
c.
\(\left(x^2-7\right)\left(x+2\right)-\left(2x-1\right)\left(x-14\right)+x\left(x^2-2x-22\right)+35=x^3+2x^2-7x-14-2x^2+28x+x-14+x^3-2x^2-22x+35\)
\(=\left(x^3+x^3\right)+\left(2x^2-2x^2\right)+\left(28x-22x-7x+x\right)+\left(35-14\right)=2x^3+21\)
a: \(=9x^2-y^2+x^2-2xy+y^2\)
\(=10x^2-2xy+2y^2\)
b: \(=4x^2-9-x^2+6x-9+2x^2+4x-x-2\)
\(=5x^2+9x-16\)
c: \(=\left(2x-1-x-1\right)^2=\left(x-2\right)^2=x^2-4x+4\)
1: \(B=10x^2-15xy-xy+5xy=10x^2-11xy\)
\(=10\cdot\dfrac{1}{25}-11\cdot\dfrac{-1}{5}\cdot\dfrac{-1}{2}\)
\(=\dfrac{2}{5}-\dfrac{11}{10}=\dfrac{-7}{10}\)
2: \(C=x^2y^2-xy^3-2x^3+2x^2y^2\)
\(=-xy^3+3x^2y^2-2x^3\)
\(=-\dfrac{-1}{2}\cdot2^3+3\cdot\left(\dfrac{-1}{2}\cdot2\right)^2-2\cdot\left(-\dfrac{1}{2}\right)^3\)
\(=\dfrac{1}{4}\cdot8+3-2\cdot\dfrac{-1}{8}\)
\(=2+3+\dfrac{1}{4}=5+\dfrac{1}{4}=\dfrac{21}{4}\)
A = 5x(x - y) - y(5x - y)
A = 5x2 - 5xy - 5xy + y2
A = 5x2 - 10xy + y2 (1)
Thay x = -1; y = 3 vào (1), ta có:
5.(-1)2 - 10.(-1).3 + 32 = 44
B = 4y(x2 - 3xy + 3y2) - 2xy(2x - 6y - 3)
B = 4x2y - 12x2 + 12y3 - 4x2y + 12xy2 + 6xy
B = 12y3 + 6xy (1)
Thay x = 5; y = -1 vào (1), ta có:
12.(-1)3 + 6.5.(-1) = -42
C = 5x2(x - y2) + 3x(xy2 - y) - 5x3
C = 5x3 - 5x2y2 + 3x2y2 - 3xy - 5x3
C = -2x2y2 - 3xy (1)
Thay x = -2; y = -5 vào (1), ta có:
-2.(-2)2.(-5)2 - 3.(-2).(-5) = -230
D = 6x2(y2 - xy + 2x2y) - 3xy(2xy - x2 + 4x3)
D = 6x2y2 - 6x3y + 12x4y - 6x2y2 + 3x3y - 12x4y
D = -3x3y (1)
Thay x = 11; y = -1 vào (1), ta có:
-3.113.(-1) = 3993
(2x2x−y−4x24x2+4xy+y2):(2x4x2−y2+1y−2x)(2x2x−y−4x24x2+4xy+y2):(2x4x2−y2+1y−2x)
=(2x2x−y−4x2(2x+y)2):(2x(2x−y)(2x+y)−12x−y)=(2x2x−y−4x2(2x+y)2):(2x(2x−y)(2x+y)−12x−y)
=(2x(2x+y)2−4x2(2x−y)(2x−y)(2x+y)2):(2x−(2x+y)(2x−y)(2x+y))=(2x(2x+y)2−4x2(2x−y)(2x−y)(2x+y)2):(2x−(2x+y)(2x−y)(2x+y))
=(8x3+8x2y+2xy2−8x3+4x2y(2x−y)(2x+y)2):(−y(2x−y)(2x+y))=(8x3+8x2y+2xy2−8x3+4x2y(2x−y)(2x+y)2):(−y(2x−y)(2x+y))
=−(12x2y+xy22x+y)=−12x2y−xy22x+y