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a) x3 + x2y - x2z - xyz
= ( x3 + x2y ) - ( x2z + xyz )
= x2( x + y ) + xz( x + y )
= ( x + y )( x2 + xz )
= x( x + y )( x + z )
b) x2 - y2 + 6x + 9
= ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x - y + 3 )( x + y + 3 )
c) x2 - 4xy - x + 2y + 4y2
= ( x2 - 4xy + 4y2 ) - ( x - 2y )
= ( x - 2y )2 - ( x - 2y )
= ( x - 2y )( x - 2y - 1 )
d) 18x3 - 12x2 + 3x - 2
= ( 18x3 - 12x2 ) + ( 3x - 2 )
= 6x2( 3x - 2 ) + ( 3x - 2 )
= ( 3x - 2 )( 6x2 + 1 )
e) a2 + 2ab + b2 - c2 + 2cd - d2
= ( a2 + 2ab + b2 ) - ( c2 - 2cd + d2 )
= ( a + b )2 - ( c - d )2
= ( a + b - c + d )( a + b + c - d )
f) xz - yz - x2 + 2xy - y2
= z( x - y ) - ( x2 - 2xy + y2 )
= z( x - y ) - ( x - y )2
= ( x - y )( z - x + y )
a) x3 + x2y - x2z - xyz
= ( x3 + x2y ) - ( x2z + xyz )
= x2( x + y ) + xz( x + y )
= ( x + y )( x2 + xz )
= x( x + y )( x + z )
b) x2 - y2 + 6x + 9
= ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x - y + 3 )( x + y + 3 )
c) x2 - 4xy - x + 2y + 4y2
= ( x2 - 4xy + 4y2 ) - ( x - 2y )
= ( x - 2y )2 - ( x - 2y )
= ( x - 2y )( x - 2y - 1 )
d) 18x3 - 12x2 + 3x - 2
= ( 18x3 - 12x2 ) + ( 3x - 2 )
= 6x2( 3x - 2 ) + ( 3x - 2 )
= ( 3x - 2 )( 6x2 + 1 )
e) a2 + 2ab + b2 - c2 + 2cd - d2
= ( a2 + 2ab + b2 ) - ( c2 - 2cd + d2 )
= ( a + b )2 - ( c - d )2
= ( a + b - c + d )( a + b + c - d )
f) xz - yz - x2 + 2xy - y2
= z( x - y ) - ( x2 - 2xy + y2 )
= z( x - y ) - ( x - y )2
= ( x - y )( z - x + y )
a) \(\left(x-9\right)\left(x-7\right)+1\)
\(=x^2-16x+63+1\)
\(=x^2-16x+64\)
\(=\left(x-8\right)^2\)
b) \(x^3+2x^2-3x-6\)
\(=x^2\left(x+2\right)-3x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-3x\right)\)
\(=x\left(x+2\right)\left(x-3\right)\)
c) \(x^2-y^2+xz-yz\)
\(=x\left(x+z\right)-y\left(y+z\right)\)
\(=\left(x-y\right)\left(y+z\right)\)
d) \(x^3-x+3x^2y+y^3-y\)
botay:(
Bài 1 :
a) xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z²)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)
b) \(x^3-x+3x^2y+3xy^2+y^3-x-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
Đã có kết quả
Bài 1,chữa phần a
xy(x+y)+yz(y+z)+xz(x+z)+2xyz
=[xy(x+y)+xyz]+[yz(y+z)+xyz]+xz(x+z)
=xy(x+y+z)+yz(x+y+z)+xz(x+z)
=y(x+y+z)(x+z)+xz(x+z)
=(x+z)(xy+y2+yz+xz)
=(x+z)(x+y)(y+z)
Chữa phần b
x3-x+3x2y+3xy2+y3-y
=(x+y)(x+y-1)(x+y+1)
Bài2
a3+b3+c3=(a+b)3-3ab(a+b)+c3=-c3-3ab(-c)+c3=3abc
Ai làm đúng như này ớ sẽ k
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)