N = (x-y)mũ 3 - xmũ2+2xy-ymũ2
K
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5 tháng 10 2020
a) ( 5x - y )( 25x2 + 5xy + y2 ) = ( 5x )3 - y3 = 125x3 - y3
b) ( x - 3 )( x2 + 3x + 9 ) - ( 54 + x3 ) = x3 - 33 - 54 - x3 = -27 - 54 = -81
c) ( 2x + y )( 4x2 - 2xy + y2 ) - ( 2x - y )( 4x2 + 2xy + y2 ) = ( 2x )3 + y3 - [ ( 2x )3 - y3 ]= 8x3 + y3 - 8x3 + y3 = 2y3
d) ( x + y )2 + ( x - y )2 + ( x + y )( x - y ) - 3x2 = x2 + 2xy + y2 + x2 - 2xy + y2 + x2 - y2 - 3x2 = y2
e) ( x - 3 )3 - ( x - 3 )( x2 + 3x + 9 ) + 6( x + 1 )2
= x3 - 9x2 + 27x - 27 - ( x3 - 33 ) + 6( x2 + 2x + 1 )
= x3 - 9x2 + 27x - 27 - x3 + 27 + 6x2 + 12x + 6
= -3x2 + 39x + 6
= -3( x2 - 13x - 2 )
f) ( x + y )( x2 - xy + y2 ) + ( x - y )( x2 + xy + y2 ) - 2x3
= x3 + y3 + x3 - y3 - 2x3
= 0
g) x2 + 2x( y + 1 ) + y2 + 2y + 1
= x2 + 2x( y + 1 ) + ( y2 + 2y + 1 )
= x2 + 2x( y + 1 ) + ( y + 1 )2
= ( x + y + 1 )2
= [ ( x + y ) + 1 ]2
= ( x + y )2 + 2( x + y ) + 1
= x2 + 2xy + y2 + 2x + 2y + 1
NA
Nhân đa thức:
a) (1/2xy-3/4).(1/2xy+3/4)
b) (2x+3).(4x mũ 2 - 6x+9)
c) (xy-2).(x mũ 2 y mũ 2 + 2xy + 4)
2
A
25 tháng 8 2020
a, \(\left(\frac{1}{2}xy-\frac{3}{4}\right)\left(\frac{1}{2}xy+\frac{3}{4}\right)=\frac{1}{4}x^2y^2+\frac{3}{8}xy-\frac{3}{8}xy-\frac{9}{16}=\frac{1}{4}x^2y^2-\frac{9}{16}\)
b, \(\left(2x+3\right)\left(4x^2-6x+9\right)=8x^3-12x^2+18x+12x^2-18x+27=8x^2+27\)
c, \(\left(xy-2\right)\left(x^2y^2+2xy+4\right)=x^3y^3+2x^2y^2+4xy-2x^2y^2-4xy-8=x^3y^3-8\)
CQ
25 tháng 8 2020
Mk ko chép đề bài ra nhé
a, = 1/2xy.( -3/4 + 3/4 )
=1/2xy.
b, Áp dụng HĐT số 2, có: (Chỗ này ko cần chép cx đc)
=(2x+3).(2x+3)^2 (^ là mũ)
=(2x+3)^3
c, Áp dụng HĐT số 2, có:
=(xy-2).(xy + 2)^2
17 tháng 9 2020
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 )
17 tháng 8 2021
h, \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)
\(\Rightarrow\left(27x^3-8\right):\left(3x-2\right)\\ =\left(3x-2\right)\left(9x^2+6x+4\right):\left(3x-2\right)\\ =9x^2+6x+4\)
g, \(x^4-2x^2+1=\left(x^2-1\right)^2\)
\(\Rightarrow\left(x^4-2x^2+1\right):\left(1-x^2\right)\\ =\left(x^2-1\right)^2:\left(1-x^2\right)\\ =x^2-1\)
NN
1
10 tháng 9 2020
1) x2 + 2xy + y2 + 2x + 2y - 15
= ( x2 + 2xy + y2 + 2x + 2y + 1 ) - 16
= [ ( x2 + 2xy + y2 ) + 2( x + y ) + 12 ] - 42
= [ ( x + y )2 + 2( x + y ) + 12 ] - 42
= ( x + y + 1 )2 - 42
= ( x + y + 1 - 4 )( x + y + 1 + 4 )
= ( x + y - 3 )( x + y + 5 )
2) x4 - x3 + x2 - 1
= ( x4 - x3 ) + ( x2 - 1 )
= x3( x - 1 ) + ( x - 1 )( x + 1 )
= ( x - 1 )[ x3 + ( x + 1 ) ]
= ( x - 1 )( x3 + x + 1 )
24 tháng 9 2020
1) x2 + x2y - y - 1
= x2( 1 + y ) - ( 1 + y )
= ( 1 + y )( x2 - 1 )
= ( 1 + y )( x - 1 )( x + 1 )
2) x2 + y2 - 2xy - 25
= ( x2 - 2xy + y2 ) - 25
= ( x - y )2 - 52
= ( x - y - 5 )( x - y + 5 )
3) ( 2x - 1 )( x2 + 2x - 1 ) - ( 1 - 2x )( x - 3 )
= ( 2x - 1 )( x2 + 2x - 1 ) + ( 2x - 1 )( x - 3 )
= ( 2x - 1 )( x2 + 2x - 1 + x - 3 )
= ( 2x - 1 )( x2 + 3x - 4 )
= ( 2x - 1 )( x2 - x + 4x - 4 )
= ( 2x - 1 )[ x( x - 1 ) + 4( x - 1 ) ]
= ( 2x - 1 )( x - 1 )( x + 4 )
4) a2 + x2 - 16 + 2ax
= ( a2 + 2ax + x2 ) - 16
= ( a + x )2 - 42
= ( a + x - 4 )( a + x + 4 )
13 tháng 5 2020
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
\(n=\left(x-y\right)^3-x^2+2xy-y^2\)
\(n=x^3-3x^2y+3xy^2-y^3-x^2+2xy-y^2\)