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a);b);c) Dùng máy tính (cụ thể là solve) bấm nghiệm rồi phân tích
d)Nhóm số T1;T2;T4 lại vs nhau
e)Biến đổi thành x2-2xy+y2-9y2
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
a) 2x3 + 6xy - x2z - 3yz
= ( 2x3 + 6xy ) - ( x2z + 3yz )
= 2x( x2 + 3y ) - z( x2 + 3y )
= ( x2 + 3y )( 2x - z )
b) x2 - 6xy + 9y2 - 49
= ( x2 - 6xy + 9y2 ) - 49
= ( x - 3y )2 - 72
= ( x - 3y - 7 )( x - 3y + 7 )
c) x3 + 4x2 + 16x + 64
= ( x3 + 4x2 ) + ( 16x + 64 )
= x2( x + 4 ) + 16( x + 4 )
= ( x + 4 )( x2 + 16 )
a) =(2x^3-x^2z)+(6xy-3yz)
=x^2(2x-z)+3y(2x-z)
=(x^2+3y)(2x-z)
b) =(x^2-6xy+9y^2)-7^2
=(x-3y)^2-7^2
=(x-3y+7)(x-3y-7)
c) =(x^3+4x^2)+(16x+64)
=x^2(x+4)+16(x+4)
=(x^2+16)(x+4)
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 )
(3x-1)2-16=(3x-1-4)(3x+1+4)
(3x+1)2-4(x-2)2=[3x+1-2(x-2)][3x+1+x(x-2)]
9(2x+3)2-4(x+1)2=[3(2x+3)-2(x+1)][3(2x+3)+2(x+1)]
-4x2+12xy-9y2+25= -(4x2-12xy+9y2-25)=-[(2x-3y)-25] = -(2x-3y+5)(2x-3y-5)
a)
\(4x^2-9y^2+6x-9y=\left(2x-3y\right)\left(2x+3\right)+3\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+3\right)\)
b)
\(1-2x+2yz+x^2-y^2-z^2=\left(x^2-2x+1\right)-\left(y^2-2yz+z^2\right)\) (đổi dấu)
\(=\left(x-1\right)^2-\left(y-z\right)^2\)
c)
\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5\left(x+1\right)+3\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)
1, x2(x2+2x+1)=x2(x+1)2
2, 2(x2+2x+1-y2)=2(x+1-y)(x+1+y)
3, 16-(x2+2xy+y2)=(4-x-y)(4+x+y)
\(x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
hk tốt
^^
a) \(x^4+x^3+2x^2+x+1=\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2+1\right)\)
b) \(4x^2-4x-3=4x^2+2x-6x-3=2x\left(2x+1\right)-3\left(2x+1\right)=\left(2x+1\right)\left(2x+3\right)\)
c) \(4x^4+81=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2=\left(2x^2-6x+9\right)\left(2x^2+6x-9\right)\)
d) \(x^2-6xy-25+9y^2=\left(x-3y\right)^2-25=\left(x-3y-5\right)\left(x-3y+5\right)\)
e) \(x^2-8y^2-2xy=x^2+2xy-4xy-8y^2=x\left(x+2y\right)-4y\left(x+2y\right)=\left(x+2y\right)\left(x-4y\right)\)