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Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
\(g,8x^3-27y^3=\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\)
\(h,x^3+y^3+2x^2-2xy+2y^2\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+2\left(x^2-xy+y^2\right)\)
\(=\left(x^2-xy+y^2\right)\left(x+y+2\right)\)
a , \(-q^3+12q^2x-48qx^2+64x^3\)
\(=-\left(q^3-12q^2x+48qx^2-64x^3\right)\)
\(=\)\(-\left(q-4x\right)^3\)
b , x2 + 2xy - y2 - 9
= - ( x2 - 2xy + y2 ) - 9
= - ( x - y )2 - 9
= ( - x + y - 3 ) ( x - y + 3 )
3 , 1 - m2 + 2mn - n2
= 1 - ( m2 - 2mn + n2 )
= 1 - ( m - n )2
= ( 1 - m + n ) ( 1 + m - n )
4 , x3 - 8 + 6a2 - 12a
= x3 + 6a2 - 12a + 8
= x3 + 6a2 - 12a + 4 + 4
= x3 + ( 6a2 - 12a + 4 ) + 4
= x3 + ( 3a - 2 )2 + 4
= ( x + 3a - 2 + 2 ) ( x2 + 3a + 2 + 2 )
( Mai làm tiếp mấy ý sau '-' muộn rồi ~ )
5 , x2 - 2xy + y2 - xz - yz
= ( x2 - 2xy + y2 ) - ( xz + yz )
= ( x - y )2 - z ( x + y )
= ( x - y ) 2 - z ( x - y )
= ( x - y ) ( x - y - z )
6 , x2 - 4xy + 4y 2 - z2 + 4z - 4t2
=( x2 - 4xy + 4y 2 ) - (z2 - 4z +4 ) . t2
= ( x - y )2 - ( z - 2 )2 . t2
= ( x - y - z - 2 ) ( x - y + z - 2 ) t2
7 , 25 - 4x2 - 4xy - y2
= 25 + ( - 4x2 - 4xy + y2 )
= 25 + ( 2x - y )2
= ( 5 + 2x - y ) ( 5 + 2x + y )
8 ,
x3 + y3 + z3 - 3xyz
= (x+y)3 - 3xy (x - y ) + z3 - 3xyz
= [ ( x + y)3 + z3 ] - 3xy ( x + y + z )
= ( x + y + z )3 - 3z ( x + y )( x + y + z ) - 3xy ( x - y - z )
= ( x + y + z )[( x + y + z )2 - 3z ( x + y ) - 3xy ]
= ( x + y + z )( x2 + y2 + z2 + 2xy + 2xz + 2yz - 3xz - 3yz - 3xy)
= ( x + y + z)(x2 + y2 + z2 - xy - xz - yz)
c) \(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
b) \(x^3+3x^2-3x-1\)
\(=\left(x^3-1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+4x+1\right)\)
Bài làm:
1) Ta có: \(2x^2+5xy+2y^2\)
\(=\left(2x^2+4xy\right)+\left(xy+2y^2\right)\)
\(=2x\left(x+2y\right)+y\left(x+2y\right)\)
\(=\left(2x+y\right)\left(x+2y\right)\)
2) Ta có: \(2x^2+2xy-4y^2\)
\(=\left(2x^2-2xy\right)+\left(4xy-4y^2\right)\)
\(=2x\left(x-y\right)+4y\left(x-y\right)\)
\(=2\left(x+2y\right)\left(x-y\right)\)
\(1)2x^2+5xy+2y^2=2x^2+4xy+xy+2y^2=\left(2x^2+4xy\right)+\left(xy+2y^2\right)=2x\left(x+2y\right)+y\left(x+2y\right)=\left(2x+y\right)\left(x+2y\right)\)\(2)2x^2+2xy-4y^2=2x^2+4xy-2xy-4y^2=\left(2x^2-2xy\right)+\left(4xy-4y^2\right)=2x\left(x-y\right)+4y\left(x-y\right)=\left(2x+4y\right)\left(x-y\right)\)
a) \(8a^2xy-18b^2xy=2xy\left(4a^2-9b^2\right)=2xy\left(2a-3b\right)\left(2a+3b\right)\)
b) \(32a^2b^2-4=4\left(8a^2b^2-1\right)\)
c) \(x^2-49z^2-4xy+4y^2=\left(x^2-4xy+4y^2\right)-49z^2\)
\(=\left(x-2y\right)^2-\left(7z\right)^2=\left(x-2y+7z\right)\left(x-2y-7z\right)\)
d) \(3x^2+6x+3-3y^2=3\left(x^2+2x+1-y^2\right)=3.\left[\left(x+1\right)^2-y^2\right]\)
\(=3\left(x-y+1\right)\left(x+y+1\right)\)
e) \(12x^2y-12y^3+36xy+27y=3y\left(4x^2-4y^2+12x+9\right)\)
\(=3y\left[\left(4x^2+12x+9\right)-4y^2\right]=3y\left[\left(2x+3\right)^2-\left(2y\right)^2\right]\)
\(=3y\left(2x-2y+3\right)\left(2x+2y+3\right)\)
a) 8a2xy - 18b2xy
= 2xy( 4a2 - 9b2 )
= 2xy( [ ( 2a )2 - ( 3b )2 ]
= 2xy( 2a - 3b )( 2a + 3b )
b) 32a2b2 - 4
= 4( 8a2b2 - 1 )
c) x2 - 49z2 - 4xy + 4y2
= ( x2 - 4xy + 4y2 ) - 49z2
= ( x - 2y )2 - ( 7z )2
= ( x - 2y - 7z )( x - 2y + 7z )
d) 3x2 + 6x + 3 - 3y2
= 3( x2 + 2x + 1 - y2 )
= 3[ ( x2 + 2x + 1 ) - y2 ]
= 3[ ( x + 1 )2 - y2 ]
= 3( x - y + 1 )( x + y + 1 )
e) 12x2y - 12y3 + 36xy + 27y
= 3y( 4x2 - 4y2 + 12x + 9 )
= 3y[ ( 4x2 + 12x + 9 ) - 4y2 ]
= 3y[ ( 2x + 3 )2 - ( 2y )2 ]
= 3y( 2x - 2y + 3 )( 2x + 2y + 3 )
Bài giải:
a) x3 – 2x2 + x = x(x2 – 2x + 1) = x(x – 1)2
b) 2x2 + 4x + 2 – 2y2 = 2[(x2 + 2x + 1) – y2]
= 2[(x + 1)2 – y2]
= 2(x + 1 – y)(x + 1 + y)
c) 2xy – x2 – y2 + 16 = 16 – (x2 – 2xy + y2) = 42 – (x – y)2
= (4 – x + y)(4 + x – y)
a) \(x^3 - 2x^2 + x\) \(= x(x^2 - 2x + 1)\)
\(= x (x - 1 )^2\)
b) \(2x^2 + 4x + 2 - 2y^2\) \(= 2(x^2 + 2x + 1 - y^2)\)
\(=2\left[\left(x^2+2x+1\right)-y^2\right]\)
\(=2\left[\left(x+1^2\right)-y^2\right]\)
\(= 2 (x+1-y) (x+1+y)\)
c) \(2xy - x^2 - y^2 + 16\) \(= - (x^2 - 2xy + y^2 - 4^2)\)
\(= - [(x^2 - 2xy + y^2) - 4^2]\)
\(= - [(x-y)^2 - 4^2 ]\)
\(= - (x - y - 4) (x- y + 4)\)
2x3y - 2xy3 - 4xy2 - 2xy
= 2xy (x2 - y2 - 2y - 1)
= 2xy [x2 - (y2 + 2y + 1)]
= 2xy [x2 - (y + 1)2]
= 2xy (x - y - 1) (x + y + 1)
\(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)