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\(1)A=2x\left(x-y\right)-y\left(y-2x\right)\)
\(=2x^2-2xy-y^2+2xy\)
\(=2x^2-y^2=2.\left(-\dfrac{2}{3}\right)^2-\left(-\dfrac{1}{3}\right)^2\)
\(=\dfrac{8}{9}-\dfrac{1}{9}=\dfrac{7}{9}\)
\(2)B=5x\left(x-4y\right)-4y\left(y-5x\right)\)
\(=5x^2-20xy-4y^2+20xy\)
\(=5x^2-4y^2=5.\left(-\dfrac{1}{5}\right)^2-4.\left(-\dfrac{1}{2}\right)^2=\dfrac{1}{5}-1=-\dfrac{4}{5}\)
\(3)C=\text{x.(x^2-y^2)-x^2(x+y)+y(x^2-x)}\)
\(=x^3-xy^2-x^3-x^2y+x^2y-xy\)
\(=-xy\left(x+1\right)\)
a) A = x2( x + y ) - y( x2 + y2 )
= x3 + x2y - x2y - y3
= x3 - y3
Với x = 1 ; y = -1
A = 13 - (-1)3 = 1 + 1 = 2
b) B = 5x( x - 4y ) - 4y( y - 5x )
= 5x2 - 20xy - 4y2 + 20xy
= 5x2 - 4y2
Với x = -0, 6 ; y = -0, 75
B = 5.(-0, 6)2 - 4.(-0, 75)2 = 5.9/25 - 4.9/16 = 9/5 - 9/4 = -9/20
C = x( x - y + 1 ) - y( y + 1 - x )
= x2 - xy + x - y2 - y + xy
= x2 + x - y2 - y
= ( x2 - y2 ) + ( x - y )
= ( x - y )( x + y ) + ( x - y )
= ( x - y )( x + y + 1 )
Thế x = -2/3 ; y = -1/3 ta được
C = [ -2/3 - (-1/3 ) ][ -2/3 - 1/3 + 1 ]
= ( -2/3 + 1/3 ).0
= 0
a, \(A=x^2\left(x+y\right)-y\left(x^2+y^2\right)+2002=x^3-y^3+2002\)
Thay x = 1; y = -1 ta có : \(1^3-\left(-1\right)^3+2002=1-1+2002=2002\)
b, \(5x\left(x-4y\right)-4y\left(y-5x\right)-\frac{11}{20}=5x^2-4y^2-\frac{11}{20}\)
Thay x = -0,6 ; y = -0,75 ta có : \(5.\left(-0,6\right)^2-4\left(-0,75\right)^2-\frac{11}{20}=-1\)
c, \(x\left(x-y+1\right)-y\left(y+1-x\right)=x^2+x-y^2-y\)
Thay x = -2/3 ; y = -1/3 ta có : \(\left(-\frac{2}{3}\right)^2-\frac{2}{3}-\left(-\frac{1}{3}\right)^2+\frac{1}{3}=0\)
a) \(A=5x\left(4x^2-2x+1\right)-2x\left(10x^2-5x-2\right)\)
\(A=20x^3-10x^2+5x-20x^3+10x^2+4x\)
\(A=9x\)
Thay x = 15 vào, ta có:
\(A=9.15=135\)
b) \(B=5x\left(x-4y\right)-4y\left(y-5x\right)\)
\(B=5x^2-20xy-4y^2+20xy\)
\(B=5x^2-4y\)
Thay \(x=-\frac{1}{5};y=-\frac{1}{2}\) vào, ta có:
\(B=5.\left(-\frac{1}{5}\right)^2-4.\left(-\frac{1}{2}\right)=\frac{11}{5}\)
c) \(C=6xy\left(xy-y^2\right)-8x^2\left(x-y^2\right)-5y^2\left(x^2-xy\right)\)
\(C=6x^2y^2-6xy^3-8x^3+8x^2y^2-5x^2y^2+5xy^3\)
\(C=9x^2y^2-xy^3-8x^3\)
Thay \(x=\frac{1}{2};y=2\) vào, ta có:
\(C=9.\left(\frac{1}{2}\right)^2.2^2-\frac{1}{2}.2^3-8.\left(\frac{1}{2}\right)^3=4\)
d) \(D=\left(3x+5\right)\left(2x-1\right)+\left(4x-1\right)\left(3x+2\right)\)
\(D=6x^2-3x+10x-5+12x^2+8x-3x-2\)
\(D=18x^2+12x-7\)
Ta có: \(\left|2\right|=\orbr{\begin{cases}x=-2\\x=2\end{cases}}\)
+) Với x = -2
\(D=18.\left(-2\right)^2+12.\left(-2\right)-7=41\)
+) Với x = 2
\(D=18.2^2+12.2-7=89\)