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D = x2 + 4xy + 4y2 - z2 + 2xt - t2
= (x + 2y)2 - (z - t)2
= (x + 2y - z + t)(x + 2y + z - t)
Thay x = 10 ; y = 40 ; z = 30 ; t = 20 vào D
\(\Rightarrow D=\left(10+40.2-30+20\right)\left(10+40.2+30-20\right)=80.100=8000\)
D = x\(^2\) + 4xy + 4y \(^2\) - z \(^2\) + 2zt - t \(^2\)
D = (x + 2y)\(^2\) - z\(^2\)+ z\(^2\) + 2zt + t\(^2\) - t\(^2\)
D = (10 + 80)\(^2\) - 30\(^2\) + (z + t)\(^2\) - 20\(^2\)
D = 90\(^2\) - 900 - 900 + (30 + 20)\(^2\) - 400
D = 8100 - 900 + 2500 - 400
D =8600
HT
D = x\(^2\) + 2xy + y\(^2\) - z\(^2\) - 2zt - t\(^2\)
D = (x + y)\(^2\) - z\(^2\) + z\(^2\) - 2zt + t\(^2\) - t\(^2\)
D = (89 + 11)\(^2\) +(z - t)\(^2\) - z\(^2\) - t\(^2\)
D = 100\(^2\) + (60 - 30)\(^2\) - 60\(^2\) - 30\(^2\)
D = 10 000 + 900 - 3600 - 900
D = 6400
Học tốt
\(A=\frac{x^2+y^2-z^2+2xy}{x^2-y^2+z^2+2xz}\)
\(=\frac{\left(x^2+2xy+y^2\right)-z^2}{\left(x^2+2xz+z^2\right)-y^2}\)
\(=\frac{\left(x+y\right)^2-z^2}{\left(x+z\right)^2-y^2}\)
\(=\frac{\left(x+y+z\right)\left(x+y+z\right)}{\left(x+y+z\right)\left(x-y+z\right)}\)
\(=\frac{x+y-z}{x-y+z}\)
Ta thay : \(x=0;y=2009;z=2010\) ta được :
\(A=\frac{0+2009-2010}{0-2009+2010}=-\frac{1}{1}=-1\)
Chúc bạn học tốt !!!
\(A=\frac{x^2+y^2-z^2+2xy}{x^2-y^2+z^2+2xz}=\frac{\left(x^2+2xy+y^2\right)-z^2}{\left(x^2+2xz+z^2\right)-y^2}=\frac{\left(x+y\right)^2-z^2}{\left(x+z\right)^2-y^2}\)
\(=\frac{\left(x+y+z\right)\left(x+y-z\right)}{\left(x+y+z\right)\left(x-y+z\right)}=\frac{x+y-z}{x-y+z}\)
Thay \(\hept{\begin{cases}x=0\\y=2009\\z=2010\end{cases}}\) vào biểu thức :
\(\Rightarrow A=\frac{0+2009-2010}{0-2009+2010}=-1\)
1 + 2xy - x2 - y2
= 1 - ( x2 - 2xy + y2 )
= 12 - ( x - y )2
= [ 1 - ( x - y ) ][ 1 + ( x - y ) ]
= ( y - x + 1 )( x - y + 1 )
a2 + b2 - c2 - d2 - 2ab + 2cd
= ( a2 - 2ab + b2 ) - ( c2 - 2cd + d2 )
= ( a - b )2 - ( c - d )2
= [ ( a - b ) - ( c - d ) ][ ( a - b ) + ( c - d ) ]
= ( a - b - c + d )( a - b + c - d )
a3b3 - 1
= ( ab )3 - 13
= ( ab - 1 )[ ( ab )2 + ab.1 + 12 ]
= ( ab - 1 )( a2b2 + ab + 1 )
x2( y - z ) + y2( z - x ) + z2( x - y )
= z2( x - y ) + x2y - x2z + y2z + y2x
= z2( x - y ) + ( x2y - y2x ) - ( x2z - y2z )
= z2( x - y ) + xy( x - y ) - z( x2 - y2 )
= z2( x - y ) + xy( x - y ) - z( x + y )( x - y )
= ( x - y )[ z2 + xy - z( x + y ) ]
= ( x - y )( z2 + xy - zx - zy )
= ( x - y )[ ( z2 - zx ) - ( zy - xy ) ]
= ( x - y )[ z( z - x ) - y( z - x ) ]
= ( x - y )( z - x )( z - y )
Phân tích à ? -.-
a) ax - bx + ab - x2
= ( ax + ab ) - ( x2 + bx )
= a( x + b ) - x( x + b )
= ( x + b )( a - x )
b) x2 - 4xy + 4y2 - 4
= ( x2 - 4xy + 4y2 ) - 4
= ( x - 2y )2 - 22
= ( x - 2y - 2 )( x - 2y + 2 )
c) ( x2 + y2 - 2 )2 - ( 2xy - 2 )2
= [ ( x2 + y2 - 2 ) - ( 2xy - 2 ) ][ ( x2 + y2 - 2 ) + ( 2xy - 2 ) ]
= ( x2 + y2 - 2 - 2xy + 2 )( x2 + y2 - 2 + 2xy - 2 )
= ( x2 - 2xy + y2 )[ ( x2 + 2xy + y2 ) - 4 ]
= ( x - y )2[ ( x + y )2 - 22 ]
= ( x - y )2( x + y - 2 )( x + y + 2 )
d) ab( x2 + y2 ) + ( a2 + b2 ) ( cái này không phân tích được ((: )
a)\(6x-9-x^2\)
\(=-\left(x^2+6x+9\right)\)
\(=-\left(x+3\right)^2\)
b)\(x^2+4y^2+4xy\)
\(=\left(x+2y\right)^2\)
c)\(x^2+8x+16\)
\(=\left(x+4\right)^2\)
d)\(9x^2-12xy+4y^2\)
\(=\left(3x-2y\right)^2\)
e)\(-25x^2y^2+10xy-1\)
\(=-\left(25x^2y^2-10xy+1\right)\)
\(=-\left(5xy-1\right)^2\)
f)\(4x^2-4x+1\)
\(=\left(2x-1\right)^2\)
j)\(x^2+6x+9\)
\(=\left(x+3\right)^2\)
h)\(9x^2-6x+1\)
\(=\left(3x-1\right)^2\)
#H
a, 6x - 9 - x2 = - x2 + 6x - 9 = - (x2 - 6x + 9) = - (x - 3)2
b, x2 + 4y2 + 4xy = x2 + 2. x . 2y + (2y)2 = (x + 2y)2
c, x2 + 8x + 16 = x2 + 2 . x . 4 + 42 = (x + 4)2
d, 9x2 - 12xy + 4y2 = (3x)2 - 2 . 3x . 2y + (2y)2 = (3x - 2y)2
e, - 25x2y2 + 10xy - 1 = - (25x2y2 - 10xy + 1) = - [(5xy)2 - 2 . 5xy + 1] = - (5xy - 1)2
f, 4x2 - 4x + 1 = (2x)2 - 2 . 2x + 1 = (2x - 1)2
j, x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
h, 9x2 - 6x + 1 = (3x)2 - 2 . 3x + 1 = (3x - 1)2
B1 : a, M = x3-3xy(x-y)-y3-x2+2xy-y2
= ( x3-y3)-3xy(x-y) -(x2-2xy+y2)
= (x-y)(x2+xy+y2)-3xy(x-y)-(x-y)2
= (x-y) [(x2+xy+y2-3xy-(x-y)]
= (x-y)[(x2-2xy+y2)-(x-y)
= (x-y)[(x-y)2-(x-y)]
= (x-y)(x-y)(x-y-1)
= (x-y)2(x-y-1)
= 72(7-1) = 49 . 6= 294
N = x2(x+1)-y2(y-1)+xy-3xy(x-y+1)-95
= x3+x2-(y3-y2)+xy-(3x2y-3xy2+3xy)-95
= x3+x2-y3+y2+xy-3x2y+3xy2-3xy-95
= (x3-y3)+(x2-2xy+y2)-(3x2y+y2)-(3x2y-3xy2)-95
=(x-y)(x2+xy+y2)+(x-y)2-3xy(x-y)-95
= (x-y)(x2+xy+y2+x-y-3xy)-95
= (x-y)[(x2-2xy+y2)+(x-y)]-95
= (x-y)[(x-y)2+(x-y)]-95
=(x-y)(x-y)(x-y+1)-95
= (x-y)2(x-y+1)-95
= 72(7+1)-95=297