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TN
3
1 tháng 10 2017
(42 - 25)2 - 9(4x2 - 9)2
= (42-52)2-32.[(2x)2-32]
=[(4-5).(4+5)]2-32.[(2x-3).(2x+3)]2
=(-9)2-[3.(2x-3).(2x+3)]2
=[-9-3.(2x-3).(2x+3)].[-9+3.(2x-3).(2x+3)]
.
1 tháng 10 2017
\(\left(16-25\right)^2-9\left(4x^2-9\right)^2=81-9\left(2x-3\right)^2\left(2x+3\right)^2\)
\(=9\left[9-\left(2x-3\right)^2\left(2x+3\right)^2\right]\)
\(=9\left[3-\left(2x-3\right)\left(2x+3\right)\right]\left[3+\left(2x-3\right)\left(2x+3\right)\right]\)
\(=9\left(3-4x^2+9\right)\cdot\left(3+4x^2-9\right)=9\left(12-4x^2\right)\left(4x^2-6\right)\)
\(=72\left(3-x^2\right)\left(2x^2-3\right)\)
Bạn kiểm tra lại xem mình có bị sai chỗ nào không?
NT
1
24 tháng 10 2016
a) \(4x^2-8x+4-9\left(x-y\right)^2\)
\(=4\left(x^2-2x+1\right)-9\left(x-y\right)^2\)
\(=\left[2\left(x-1\right)\right]^2-\left[3\left(x-y\right)\right]^2\)
\(=\left(2x-2+3x-3y\right)\left(2x-2-3x+3y\right)\)
\(=\left(5x-3y-2\right)\left(3y-x-2\right)\)
b) \(x^3-4x^2+12x-27\)
\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
HT
5 tháng 8 2017
a) \(\left(a^2+4\right)^2-\left(4a\right)^2\)
\(=\left(a^2+4-4a\right)\left(a^2+4+4a\right)\)
\(=\left(a-2\right)^2\left(a+2\right)^2\)
b) \(36x^2-\left(x^2+9\right)^2\)
\(=\left(6x\right)^2-\left(x^2+9\right)^2\)
\(=-\left(6x+x^2+9\right)\left(6x+x^2+9\right)\)
\(=\left(x^2-6x+9\right)\left(x^2+6x+9\right)\)
\(=\left(x-3\right)^2\left(x+3\right)^2\)
c) \(\left(4x^2-25\right)^2-9\left(2x-5\right)^2\)
\(=\left(4x^2-25\right)-\left(18x-45\right)^2\)
\(=\left(4x^2-25-18x+45\right)\left(4x^2-25+18x-45\right)\)
\(=\left(4x^2-18x+20\right)\left(4x^2+18x-70\right)\)
d) \(4\left(2x-3\right)^2-9\left(4x^2-9\right)^2\)
\(=\left(8x-12\right)^2-\left(36x^2-81\right)^2\)
\(=\left(8x-12-36x^2+81\right)\left(8x-12+36x^2-81\right)\)
còn lại tự làm
30 tháng 9 2018
\(\left(a^2+4\right)^2-16a^2\)
\(=\left(a^2+4-4a\right)\left(a^2+4+4a\right)\)
\(=\left(a^2-2.a.2+2^2\right).\left(a^2+2.a.2+2^2\right)\)
\(=\left(a-2\right)^2\left(a+2\right)^2\)
hk tốt
^^
5 tháng 9 2020
a) ( x2 - 25 )2 - ( x - 5 )2
= [ ( x - 5 )( x + 5 ) ]2 - ( x - 5 )2
= [ ( x - 5 )( x + 5 ) - ( x - 5 ) ][ ( x - 5 )( x + 5 ) + ( x - 5 ) ]
= ( x - 5 )( x + 5 - 1 )( x - 5 )( x + 5 + 1 )
= ( x - 5 )2( x + 4 )( x + 6 )
b) ( 4x2 - 25 )2 - 9( 2x - 5 )2
= ( 4x2 - 25 )2 - 32( 2x - 5 )2
= ( 4x2 - 25 )2 - ( 6x - 15 )2
= [ ( 4x2 - 25 ) - ( 6x - 15 ) ][ ( 4x2 - 25 ) + ( 6x - 15 ) ]
= ( 4x2 - 25 - 6x + 15 )( 4x2 - 25 + 6x - 15 )
= ( 4x2 - 6x - 10 )( 4x2 + 6x - 40 )
= ( 4x2 + 4x - 10x - 10 )( 4x2 + 16x - 10x - 40 )
= [ 4x( x + 1 ) - 10( x + 1 ) ][ 4x( x + 4 ) - 10( x + 4 ) ]
= ( x + 1 )( 4x - 10 )( x + 4 )( 4x - 10 )
= ( 4x - 10 )2( x + 1 )( x + 4 )
c) 4( 2x - 3 )2 - 9( 4x2 - 9 )2
= 22( 2x - 3 )2 - 32( 4x2 - 9 )2
= ( 4x - 6 )2 - ( 12x2 - 27 )2
= [ ( 4x - 6 ) - ( 12x2 - 27 ) ][ ( 4x - 6 ) + ( 12x2 - 27 ) ]
= ( 4x - 6 - 12x2 + 27 )( 4x - 6 + 12x2 - 27 )
= ( -12x2 + 4x + 21 )( 12x2 + 4x - 33 )
= ( -12x2 + 18x - 14x + 21 )( 12x2 - 18x + 22x - 33 )
= [ -12x( x - 3/2 ) - 14( x - 3/2 ) ][ 12x( x - 3/2 ) + 22( x - 3/2 ) ]
= ( x - 3/2 )( -12x - 14 )( x - 3/2 )( 12x + 22 )
= ( x - 3/2 )2( -12x - 14 )( 12x + 22 )
d) a6 - a4 + 2a3 + 2a2
= a2( a4 - a2 + 2a + 2 )
= a2( a4 - 2a3 + 2a3 + 2a2 - 4a2 + a2 + 4a - 2a + 2 )
= a2[ ( a4 - 2a3 + 2a2 ) + ( 2a3 - 4a2 + 4a ) + ( a2 - 2a + 2 ) ]
= a2[ a2( a2 - 2a + 2 ) + 2a( a2 - 2a + 2 ) + 1( a2 - 2a + 2 ) ]
= a2( a2 + 2a + 1 )( a2 - 2a + 2 )
= a2( a + 1 )2( a2 - 2a + 2 )
e) ( 3x2 + 3x + 2 )2 - ( 3x2 + 3x - 2 )2
= [ ( 3x2 + 3x + 2 ) - ( 3x2 + 3x - 2 ) ][ ( 3x2 + 3x + 2 ) + ( 3x2 + 3x - 2 ) ]
= ( 3x2 + 3x + 2 - 3x2 - 3x + 2 )( 3x2 + 3x + 2 + 3x2 + 3x - 2 )
= 4( 6x2 + 6x )
= 4.6x( x + 1 )
= 24( x + 1 )
DH
3
3 tháng 8 2021
\(16y^2-4x^2-12x-9=16y^2-\left(2x-3\right)^2\)
\(=\left(4y-2x+3\right)\left(4y+2x-3\right)\)
TT
3
24 tháng 9 2018
\(4x^2-9+\left(2x+3\right)^2=\left(2x-3\right)\left(2x+3\right)+\left(2x+3\right)^2\)
\(=\left(2x+3\right)\left[\left(2x-3\right)+\left(2x+3\right)\right]\)
\(=4x\left(2x+3\right)\)
24 tháng 9 2018
\(4x^2-9+\left(2x+3\right)^2\)
\(=\left(2x-3\right)\left(2x+3\right)+\left(2x+3\right)^2\)
\(=\left(2x+3\right)\left(2x-3+2x+3\right)\)
\(=4x\left(2x+3\right)\)
=.= hok tốt!!
2 tháng 10 2020
a) ( 4x2 - 3x - 18 )2 - ( 4x2 + 3x )2
= [ ( 4x2 - 3x - 18 ) - ( 4x2 + 3x ) ][ ( 4x2 - 3x - 18 ) + ( 4x2 + 3x ) ]
= ( 4x2 - 3x - 18 - 4x2 - 3x )( 4x2 - 3x - 18 + 4x2 + 3x )
= ( -6x - 18 )( 8x2 - 18 )
= -6( x + 3 ).2( 4x2 - 9 )
= -12( x + 3 )( 2x - 3 )( 2x + 3 )
b) 9( x + y - 1 )2 - 4( 2x + 3y + 1 )2
= 32( x + y - 1 )2 - 22( 2x + 3y + 1 )2
= [ 3( x + y - 1 ) ]2 - [ 2( 2x + 3y + 1 ) ]2
= ( 3x + 3y - 3 )2 - ( 4x + 6y + 2 )2
= [ ( 3x + 3y - 3 ) - ( 4x + 6y + 2 ) ][ ( 3x + 3y - 3 ) + ( 4x + 6y + 2 ) ]
= ( 3x + 3y - 3 - 4x - 6y - 2 )( 3x + 3y - 3 + 4x + 6y + 2 )
= ( -x - 3y - 5 )( 7x + 9y - 1 )
c) -4x2 + 12xy - 9y2 + 25
= 25 - ( 4x2 - 12xy + 9y2 )
= 52 - ( 2x - 3y )2
= [ 5 - ( 2x - 3y ) ][ 5 + ( 2x - 3y ) ]
= ( 5 - 2x + 3y )( 5 + 2x - 3y )
d) x2 - 2xy + y2 - 4m2 + 4mn - n2
= ( x2 - 2xy + y2 ) - ( 4m2 - 4mn + n2 )
= ( x - y )2 - ( 2m - n )2
= [ ( x - y ) - ( 2m - n ) ][ ( x - y ) + ( 2m - n ) ]
= ( x - y - 2m + n )( x - y + 2m - n )
ND
4
24 tháng 8 2017
Đổi dấu – (4yx2 + yz2)(z – y2) = (4yx2 + yz2)( y2 – z), ta có thừa số
(y2 – z) chung:
C = (y2 – z)(2x2y – yz) – (4yx2 + yz2)(z – y2) + 6x2z(y2 – z)
= (y2 – z)(2x2y – yz) + (4yx2 + yz2)( y2 – z) + 6x2z(y2 – z)
= (y2 – z)[( 2x2y – yz ) + (4yx2 + yz2) + 6x2z]
= (y2 – z)[ 2x2y + 4yx2 + 6x2z]
= (y2 – z)[ 2xy2 + 4yx2 + 6x2z]
= (y2 – z)[ 2x2(y + 2y + 3z)]
= (y2 – z)[ 2x2(3y + 3z)]
= (y2 – z) 2x2 .3(y + z)
= 6x2(y2 – z)(y + z).
24 tháng 8 2017
a) 7x2 - 4x
= x ( 7x - 4 )
b) 5x2 - 2x + 10 xy - 4y
= x ( 5x - 2 ) + 2y ( 5x - 2 )
= ( x + 2y ) ( 5x - 2 )
ND
1
24 tháng 8 2017
Ta nhân thấy nghiệm của f(x) nếu có thì x = 
Cách 1:
x3 – x2 – 4 =(x3-2x2)+(x2-2x)+(2x-4)=x2(x-2)+x(x-2)+2(x-2)=(x-2)(x2+x+2)
Cách 2:
(x-2)[(x2+2x+4)-(x+2)]=(x-2)(x2+x+2)
x3-x2-4=x3-8-x2+4=(x3-8)-(x2-4)=(x-2)(x2+2x+4)-(x-2)(x+2)
\(\left(4x^2-25\right)^2-9\left(4x^2-9\right)^2\)
\(=\left(4x^2-25\right)^2-\left(12x^2-27\right)^2\)
\(=\left(4x^2-25+12x^2-27\right)\left(4x^2-25-12x^2+27\right)\)
\(=\left(16x^2-52\right)\left(2-8x^2\right)\)
\(=8\left(4x^2-13\right)\left(1-4x^2\right)\)
\(=8\left(4x^2-13\right)\left(1+2x\right)\left(1-2x\right)\)