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1) x2 - 2xy + y2 - x2
=(x - y)2 - x2
=(x - y - x)(x - y + x)= -y(2x - y)
2) x2 - 2xy - 4z2 + y2
= x2 - 2xy + y2 - 4z2
= (x - y)2 - (2z)2 = (x - y - 2z)(x - y + 2z)
3) (2x + 1)2 - (x - 1)2
=(2x + 1 - x + 1)(2x + 1 + x - 1)=3x(x + 2)
4) 4a2 - 4a + 1=(2a - 1)2
5) -9x2 + 6xy - y2
= - (9x2 - 6xy + y2)= - (3x - y)2
6) -6x + 9 + x2
= x2 - 6x + 9 = (x - 3)2
7) 4x2 - 4x + 1 - y2
= (2x - 1)2 - y2 = (2x - 1 - y)(2x - 1 + y)
pn kt lại nha
1) =(x+2)(x-2)+(x-2)2=(x-2)(x+2+x-2)=2x(x+2)
2)=x(x2-6x+9)=x(x-3)2
3)xem lại đề giúp mik
4)=x4+4x2-4x2+4=(x4+4x2+4)-4x2=(x2+2)2-4x2=(x2+2x+2)(x2-2x+2)
\(x^2-4+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2+x-2\right)\)
\(=2x\left(x-2\right)\)
\(x^2-2xy+y^2-a^2+4ab-4b^2\)
\(=\left(x-y\right)^2-\left(a-2b\right)^2\)
\(=\left(x-y-a+2b\right)\left(x-y+a-2b\right)\)
hk tốt
^^
Áp dụng HĐT a2 - b2 = ( a - b )( a + b )
và tính chất an.bn = ( a.b )n ( với n ∈ N* )
a) ( 3x + 1 )2 - ( x + 1 )2
= [ ( 3x + 1 ) - ( x + 1 ) ][ ( 3x + 1 ) + ( x + 1 ) ]
= ( 3x + 1 - x - 1 )( 3x + 1 + x + 1 )
= 2x( 4x + 2 )
= 2x.2( 2x + 1 )
= 4x( 2x + 1 )
b) ( x + y )2 - ( x - y )2
= [ ( x + y ) - ( x - y ) ][ ( x + y ) + ( x - y ) ]
= ( x + y - x + y )( x + y + x - y )
= 2y.2x = 4xy
c) ( 2xy + 1 )2 - ( 2x + y )2
= [ ( 2xy + 1 ) - ( 2x + y ) ][ ( 2xy + 1 ) + ( 2x + y ) ]
= ( 2xy + 1 - 2x - y )( 2xy + 1 + 2x + y )
= [ ( 2xy - 2x ) - ( y - 1 ) ][ ( 2xy + 2x ) + ( y + 1 ) ]
= [ 2x( y - 1 ) - ( y - 1 ) ][ 2x( y + 1 ) + ( y + 1 ) ]
= ( y - 1 )( 2x - 1 )9 y + 1 )( 2x + 1 )
d) 9( x - y )2 - 4( x + y )2
= 32( x - y )2 - 22( x + y )2
= [ 3( x - y ) ]2 - [ 2( x + y ) ]2
= ( 3x - 3y )2 - ( 2x + 2y )2
= [ ( 3x - 3y ) - ( 2x + 2y ) ][ ( 3x - 3y ) + ( 2x + 2y ) ]
= ( 3x - 3y - 2x - 2y )( 3x - 3y + 2x + 2y )
= ( x - 5y )( 5x - y )
e) ( 3x - 2y )2 - ( 2x - 3y )2
= [ ( 3x - 2y ) - ( 2x - 3y ) ][ ( 3x - 2y ) + ( 2x - 3y ) ]
= ( 3x - 2y - 2x + 3y )( 3x - 2y + 2x - 3y )
= ( x + y )( 5x - 5y )
= ( x + y )5( x - y )
f) ( 4x2 - 4x + 1 ) - ( x + 1 )2
= ( 2x - 1 )2 - ( x + 1 )2
= [ ( 2x - 1 ) - ( x + 1 ) ][ ( 2x - 1 ) + ( x + 1 ) ]
= ( 2x - 1 - x - 1 )( 2x - 1 + x + 1 )
= 3x( x - 2 )
a) \(=\left(x-2y\right)\left(x^2+5x\right)\)
b) \(=\left(x-1\right)\left(x^2+2x+1\right)=\left(x-1\right)\left(x+1\right)^2\)
c) \(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(3-x+3\right)\)
\(=\left(x+3\right)\left(6-x\right)\)
e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)
f) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
x2 - 2xy + y2 - x2
= (x - y)2 - x2
= (x - y -x) (x - y + x)
= -y(2x -y)
x2 - 2xy - 4x2 + y2
= (x2 - 2xy + y2) - 4x2
= (x - y)2 - 4x2
= (x - y - 2x)(x - y +2x)
(2x + 1 )2 - ( x - 1)2
= (2x + 1 - x + 1)(2x + 1 + x - 1)
= 3x( x + 2)
4a2 - 4a + 1
= (2a - 1)2
-9x2 + 6xy - y2
= - (9x2 - 6xy + y2)
= - (3x - y)2
-6x + 9 + x2
= x2 - 6x + 9
= (x - 3)2
4x2 - 4x + 1 - y2
= (2x - 1)2 - y2
= (2x - 1 - y2)(2x - 1 + y2)