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21 tháng 10 2018
a)\(6x^2-9xy\)
\(=3x\left(2x-3y\right)\)
b)\(x^2-y^2-3x+3y\)
\(=\left(x-y\right)\left(x+y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-3\right)\)
21 tháng 10 2018
c)\(x^4-8x^2-9\)
\(=x^4+x^2-9x^2-9\)
\(=x^2\left(x^2+1\right)-9\left(x^2+1\right)\)
\(=\left(x^2-9\right)\left(x^2+1\right)\)
\(=\left(x+3\right)\left(x-3\right)\left(x^2+1\right)\)
d)\(x^4-4\left(x^2+5\right)-25\)
\(=\left(x^2-5\right)\left(x^2+5\right)-4\left(x^2+5\right)\)
\(=\left(x^2+5\right)\left(x^2-5-4\right)\)
\(=\left(x^2+5\right)\left(x^2-9\right)\)
\(=\left(x^2+5\right)\left(x-3\right)\left(x+3\right)\)
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?
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 )
16 tháng 8 2018
\(\left(x-5\right)^2-16=\left(x-5\right)^2-4^2=\left(x-5-4\right)\left(x-5+4\right)=\left(x-9\right)\left(x-1\right)\)
\(25-\left(3-x\right)^2=5^2-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)
\(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)=\left(5x-5\right)\left(9x-3\right)=15\left(x-1\right)\left(3x-1\right)\)\(49\left(y-4\right)^2-9\left(y+2\right)^2=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2=\left(7y-28-3y-6\right)\left(7y-28+3y-6\right)=\left(4y-34\right)\left(10y-22\right)\)\(=4.\left(2y-17\right)\left(5y-11\right)\)
e); f) Áp dụng hằng đẳng thức số 6,7 để làm
ML
8 tháng 8 2015
a)x4-4(x2+5)-25=x4-4x2-45=(x4-9x2)+(5x2-45)=x2(x2-9)+5(x2-9)=(x2-9)(x2+5)=(x-3)(x+3)(x2+5)
b)a2-b2-2a+1=(a2-2a+1)-b2=(a-1)2-b2=(a-b-1)(a+b-1)
c)x2-2x-4y2-4y=(x2-2x+1)-(4y2+4y+1)=(x-1)2-(2y+1)2=(x-1-2y-1)(x-1+2y+1)=(x-2y-2)(x+2y)
d)x2+4x-y2+4=(x2+4x+4)-y2=(x+2)2-y2=(x-y+2)(x+y+2)
10 tháng 8 2021
a, \(\left(x+1\right)^2-25=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
b, \(\left(xy+4\right)^2-4\left(x+y\right)^2=\left(xy+4\right)^2-\left(2x+2y\right)^2=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)
c, xem lại đề nhé
TN
1
1 tháng 10 2017
\(\left(4x^2-25\right)^2-9\left(4x^2-9\right)^2\)
\(=\left(4x^2-25\right)^2-\left(12x^2-27\right)^2\)
\(=\left(4x^2-25+12x^2-27\right)\left(4x^2-25-12x^2+27\right)\)
\(=\left(16x^2-52\right)\left(2-8x^2\right)\)
\(=8\left(4x^2-13\right)\left(1-4x^2\right)\)
\(=8\left(4x^2-13\right)\left(1+2x\right)\left(1-2x\right)\)
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
^^
giúp mình với
\(4)25-1^2=\left(5-1\right)\left(5+1\right)=4.6=24\\ 5)a^2-9=a^2-3^2=\left(a-3\right)\left(a+3\right)\)