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1) x3 + y3 + z3 - 3xyz
= ( x + y )3 - 3xy( x + y ) + z3 - 3xyz
= [ ( x + y )3 + z3 ) - [ 3xy( x + y ) + 3xyz ]
= ( x + y + z )[ ( x + y )2 - ( x + y )z + z2 ] - 3xy( x + y + z )
= ( x + y + z )( x2 + y2 + z2 + 2xy - xz - yz - 3xy )
= ( x + y + z )( x2 + y2 + z2 - xy - yz - xz )
2) Tạm thời đang bí chưa làm được :(
3) ( x2 - 2x )2( x2 - 2x - 1 ) - 6 ( đề có vấn đề -- )
4) x4 - 7x3 + 14x2 - 7x + 1
= x4 - 3x2 - 4x2 + x2 + 12x2 + x2 - 4x - 3x + 1
= ( x4 - 3x2 + x2 ) - ( 4x3 - 12x2 + 4x ) + ( x2 - 3x + 1 )
= x2( x2 - 3x + 1 ) - 4x( x2 - 3x + 1 ) + ( x2 - 3x + 1 )
= ( x2 - 3x + 1 )( x2 - 4x + 1 )
A= x4 + 64
A= (x2)2 + 2.x2.8 +82 - (2.x2 .8)
A=(x2+8)2 -16x2
A =(x2+8+4x).(x2+8-4x)
-
G=(x2+y2+z2)2 (có sẵn hdt rồi mak_)
Bài 1: 4a2-4ab+b2-9a2b2
=(2a)2-2.2a.b+b2-(3ab)2
=(2a-b)2-(3ab)2
=(2a-b-3ab)(2a-b+3ab)
a/ (4a2-4ab+b2)-9a2b2
= (2a-b)2-(3ab)2
= (2a-b-3ab) (2a-b+3ab)
a/ \(x^2\left(y-z\right)-y^2\left(y-z+x-y\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)\)
\(=\left(x^2-y^2\right)\left(y-z\right)-\left(x-y\right)\left(y^2-z^2\right)\)
\(=\left(x-y\right)\left(y-z\right)\left(x+y-y-z\right)\)
\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
b/ \(2a^3+7a^2b+7ab^2+2b^3\)
\(=2a^3+3a^2b+ab^2+4a^2b+6ab^2+2b^3\)
\(=a\left(2a^2+3ab+b^2\right)+2b\left(2a^2+3ab+b^2\right)\)
\(=\left(a+2b\right)\left(2a^2+3ab+b^2\right)=\left(a+2b\right)\left(2a^2+ab+2ab+b^2\right)\)
\(=\left(a+2b\right)\left(a\left(2a+b\right)+b\left(2a+b\right)\right)=\left(a+2b\right)\left(a+b\right)\left(2a+b\right)\)
c/ \(x^3-x^2-14x+24=x^3+x^2-12x-2x^2-2x+24\)
\(=x\left(x^2+x-12\right)-2\left(x^2+x-12\right)=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right)\left(x^2-3x+4x-12\right)=\left(x-2\right)\left(x\left(x-3\right)+4\left(x-3\right)\right)\)
\(=\left(x-2\right)\left(x-3\right)\left(x+4\right)\)
d/ \(x^3+y^3+z^3-3xyz=x^3+3x^2y+3xy^2+y^3+z^3-3xy\left(x+y\right)-3xyz\)
\(=\left(x+y\right)^3+z^3-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(\left(x+y\right)^2-\left(x+y\right)z+z^2\right)-3xy\left(x+y+z\right)\)
\(\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)
e/ \(x^4+2019x^2+2018x+2019=x^4-x+2019x^2+2019x+2019\)
\(=x\left(x^3-1\right)+2019\left(x^2+x+1\right)=x\left(x-1\right)\left(x^2+x+1\right)+2019\left(x^2+x+1\right)\)
\(=\left(x^2-x+2019\right)\left(x^2+x+1\right)\)