phân tích đa thức sau thành nhân tử
a, 81 - ( 3x + 2 ) mũ 2
b, ( 7x - 4 ) mũ 2 - ( 2x + 1 ) mũ 2
c, 9 ( x - 5y ) mũ 2 - 16 ( x + y ) mũ 2
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20 tháng 11 2021
\(a,x^2y-8x+xy-8=xy\left(x+1\right)-8\left(x+1\right)=\left(xy-8\right)\left(x+1\right)\\ b,=\left(x+3y\right)^2-9=\left(x+3y-3\right)\left(x+3y+3\right)\)
\(A=3x^2\left(2x^2-7x-2\right)-6x^2\left(x^2-4x-1\right)-3x^3+15\\ A=6x^4-21x^3-6x^2-6x^4+24x^3+6x^2-3x^3+15\\ A=15\left(đpcm\right)\)
\(Sửa:\left(6x^3-7x^2+2x\right):\left(2x+1\right)\\ =\left(6x^3+3x^2-10x^2-5x\right):\left(2x+1\right)\\ =\left[3x^2\left(2x+1\right)-5x\left(2x+1\right)\right]:\left(2x+1\right)\\ =3x^2-5x\)
QA
5 tháng 8 2021
Trả lời:
a, 5x2 + 10xy + 5y2 = 5 ( x2 + 2xy + y2 ) = 5 ( x + y )2
b, x2 + 3x - y2 + 3y = ( x2 - y2 ) + ( 3x + 3y ) = ( x - y )( x + y ) + 3 ( x + y ) = ( x + y )( x - y + 3 )
c, x2 + 5x - y2 + 5y = ( x2 - y2 ) + ( 5x + 5y ) = ( x - y )( x + y ) + 5 ( x + y ) = ( x + y )( x - y + 5 )
d, 3x2 - 3y2 - 2 ( x - y )2 = 3 ( x2 - y2 ) - 2 ( x - y )2 = 3 ( x - y )( x + y ) - 2 ( x - y )2 = ( x - y )[ 3 ( x + y ) - 2 ] = ( x - y )( 3x + 3y - 2 )
e, x2 - 2x - 4y2 - 4y = ( x2 - 4y2 ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2 ( x + 2y ) = ( x + 2y )( x - 2y - 2 )
AD
5 tháng 8 2021
a) 5x2+10xy+5y2
=5(x2+2xy+y2)
=5(x+y)2
b) x2+3x-y2+3y
=(x2-y2)+(3x+3y)
=(x-y)(x+y)+3(x+y)
=(x+y)(x-y+3)
c) x2+5x-y2+5y
=(x2-y2)+(5x+5y)
=(x-y)(x+y)+5(x+y)
=(x+y)(x-y+5)
d) 3x2-3y2-2(x-y)2
=3(x2-y2)-2(x-y)2
=3(x-y)(x+y)-2(x-y)2
=(x-y)[3(x+y)-2(x-y)]
e) x2-2x-4y2-4y
=(x2-4y2)-(2x+4y)
=(x-2y)(x+2y)-2(x+2y)
=(x+2y)(x-2y-2)
#H
5 tháng 8 2021
k) = x( 2x - 1 ) - 3y( 2x - 1 ) = ( 2x - 1 )( x - 3y )
l) = x( x - y ) + 5( x - y ) = ( x - y )( x + 5 )
m) = ( a2 - 4a + 4 )( a2 + 4a + 4 ) = ( a - 2 )2( a + 2 )2
n) = y2( x2 - 1 ) - ( x2 - 1 ) = ( x - 1 )( x + 1 )( y - 1 )( y + 1 )
q) = 3[ ( x - y )2 - 4z2 ] = 3( x - y - 2z )( x - y + 2z )
BA
30 tháng 7 2021
\(a,x^2+7x+7y-y^2\)
\(=x^2-y^2+7\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(b,x^2-2x-9y^2+6y\)
\(=x^2-\left(3y\right)^2-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-2\right)\)
\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)
\(=x\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x+x^2+xy+y^2\right)\)
31 tháng 7 2021
\(1,x^2-y^2+4x-4y\)
\(\left(x-y\right)\left(x+y\right)+4\left(x-y\right)\)
\(\left(x-y\right)\left(x+y+4\right)\)
\(x^2+2x-4y^2-4y\)
\(\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)\)
\(\left(x-2y\right)\left(x+2y+2\right)\)
\(3,3x^2-4y+4x-3y^2\)
\(3\left(x^2-y^2\right)-4\left(x-y\right)\)
\(3\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\)
\(\left(x-y\right)\left(3x+3y-4\right)\)
\(x^4-6x^3+54x-81\)
\(x^4+3x^3-9x^3+27x^2-27x^2+81x-27x-81\)
\(\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27x+81\right)\)
\(x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)
\(\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)
\(\left(x+3\right)\left(x-3\right)^3\)
QA
2 tháng 8 2021
Trả lời:
5, x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y ) ( x + 2 + y )
6, x2 + 2x - 4y2 - 4y
= ( x2 - 4y2 ) + ( 2x - 4y )
= ( x - 2y ) ( x + 2y ) + 2 ( x - 2y )
= ( x - 2y ) ( x + 2y + 2 )
7, 3x2 - 4y + 4x - 3y2
= ( 3x2 - 3y2 ) + ( 4x - 4y )
= 3 ( x2 - y2 ) + 4 ( x - y )
= 3 ( x - y ) ( x + y ) + 4 ( x - y )
= ( x - y ) [ 3 ( x + y ) + 4 ]
= ( x - y ) ( 3x + 3y + 4 )
8, x4 - 6x3 + 54x - 81
= ( x4 - 81 ) - ( 6x3 - 54x )
= ( x2 - 9 ) ( x2 + 9 ) - 6x ( x2 - 9 )
= ( x2 - 9 ) ( x2 + 9 - 6x )
= ( x - 3 ) ( x + 3 ) ( x - 3 )2
= ( x - 3 )3 ( x + 3 )
2 tháng 8 2021
a, \(x^2-y^2+4x+4=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
b, \(x^2+2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)=\left(x-2y\right)\left(x+2+2y\right)\)
c, \(3x^2-4y+4x-3y^2=3\left(x-y\right)\left(x+y\right)-4\left(y-x\right)=\left(x-y\right)\left(3x+3y+4\right)\)
d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x^2-6x+9\right)=\left(x-3\right)^3\left(x+3\right)\)
30 tháng 7 2021
1, \(x^2\left(x-3\right)-4x+12=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)
2, \(2a\left(x+y\right)-x-y=2a\left(x+y\right)-\left(x+y\right)=\left(2a-1\right)\left(x+y\right)\)
3, \(2x-4+5x^2-10x=2\left(x-2\right)+5x\left(x-2\right)=\left(2+5x\right)\left(x-2\right)\)
4, sửa đề :
\(6x^2-12x-7x+14=6x\left(x-2\right)-7\left(x-2\right)=\left(6x-7\right)\left(x-2\right)\)
5, \(xy-y^2-3x+3y=y\left(x-y\right)-3\left(x-y\right)=\left(y-3\right)\left(x-y\right)\)
AD
30 tháng 7 2021
a) x2(x-3)-4x+12
=x2(x-3)-4(x-3)
=(x-3)(x2-4)
=(x-3)(x-2)(x+2)
b) 2a(x+y)-x-y
=2a(x+y)-(x+y)
=(x+y)(2a-1)
c) 2x-4+5x2-10x
=2(x-2)+5x(x-2)
=(x-2)(2+5x)
d) 5x2-12x-7x+14
=5x2-19x+14
e) xy-y2-3x+3y
=y(x-y)-3(x-y)
=(x-y)(y-3)
#H
a) \(81-\left(3x+2\right)^2=9^2-\left(3x+2\right)^2=\left(9-3x-2\right)\left(9+3x+2\right)=\left(7-3x\right)\left(11+3x\right)\)
b) \(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)
\(=\left(5x-5\right)\left(9x-3\right)=15\left(x-1\right)\left(3x-1\right)\)
c) \(9\left(x-5y\right)^2-16\left(x+y\right)^2=\left[3\left(x-5y\right)-4\left(x+y\right)\right]\left[3\left(x-5y\right)+4\left(x+y\right)\right]\)
\(=\left(-x-19y\right)\left(7x-11y\right)\)