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a) \(3xy^2-12xy+12x\)
\(=3x\left(y-4y+4\right)\)
b) \(3x^3y-6x^2y-3xy^3-6axy^2-3a^2xy+3xy\)
\(=3xy\left(x^2-2x-y^2-2ay-a^2+1\right)\)
\(=3xy\left[\left(x^2-2\cdot x\cdot1+1^2\right)-\left(y^2+2\cdot y\cdot a+a^2\right)\right]\)
\(=3xy\left[\left(x-1\right)^2-\left(y+a\right)^2\right]\)
\(=3xy\left(x-1-y-a\right)\left(x-1+y+a\right)\)
c) \(36-4a^2+20ab-25b^2\)
\(=6^2-\left[\left(2a\right)^2-2\cdot2a\cdot5b+\left(5b\right)^2\right]\)
\(=6^2-\left(2a-5b\right)^2\)
\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)
d) \(5a^3-10a^2b+5ab^2-10a+10b\)
\(=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)\)
\(=5a\left(a-b\right)^2-10\left(a-b\right)\)
\(=\left(a-b\right)\left[5a\left(a-b\right)-10\right]\)
\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)
\(=5\left(a-b\right)\left(a^2-ab-2\right)\)
a. 3xy2-12xy+12x
= 3x(y2-4y+4)
= 3x(y-2)2
b. 3x3y-6x2y-3xy3-6axy2-3a2xy+3xy
= 3xy( x2-2x-y2-2ay-a2+1)
= 3xy ((x2-2x+1)-(a2-2ay-y2))
=3xy((x-1)2-(a-y)2)
= 3xy((x-1+a-y)(x-1-(a-y))
=3xy(x-1+a-y)(x-1-a+y)
d. =( 5a(a2-2ab+b2))-(10(a+b))
= 5a(a-b)2-10(a-b)
=5a(a-b)(a-b)-10(a-b)
=(a-b)(5a(a-b)-10)
Hình như mik làm sai hết rồi
b: \(=ab^2+ac^2+abc+bc^2+ba^2+abc+a^2c+b^2c+abc\)
\(=ab\left(a+b+c\right)+bc\left(a+b+c\right)+ac\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(ab+bc+ac\right)\)
a: \(=\left(x^2-x^2y^2\right)+\left(y^2-y\right)+\left(xy-x\right)\)
\(=-x^2\left(y-1\right)\left(y+1\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=\left(y-1\right)\left(-x^2y-x^2+y+x\right)\)
\(=\left(1-y\right)\left(x^2y+x^2-x-y\right)\)
\(=\left(1-y\right)\cdot\left[y\left(x-1\right)\left(x+1\right)+x\left(x-1\right)\right]\)
\(=\left(1-y\right)\left(x-1\right)\left(xy+y+x\right)\)
a) = (xyz+xy) +(z+1) +(yz+zx)+(x+y)
= xy(z+1) +(z+1)+z(x+y)+(x+y)
= (z+1)(xy+1)+(x+y)(Z+1)
=(z+1)(xy+1+x+y)
1) \(x^2\left(a-b\right)m-2xy\left(a-b\right)+ay^2-by^2=\left(a-b\right)x^2m-\left(a-b\right)2xy+\left(a-b\right)y^2=\left(a-b\right)\left(x^2m-2xy+y^2\right)\)
2) \(10a^3-10a=10a\left(a^2-1\right)=10a\left(a+1\right)\left(a-1\right)\)
3) \(16a^3xy-54b^3xy^4=2xy\left(8a^3-27b^3y^3\right)=2xy\left(2a-3by\right)\left(4a^2+6aby+9b^2y^2\right)\)
4) \(16+2x^3y^3=2\left(8+x^3y^3\right)=2\left(2+xy\right)\left(4+2xy+x^2y^2\right)\)
5) \(\left(a+b\right)^3+c^3=\left(a+b+c\right)\left(\left(a+b\right)^2+\left(a+b\right)c+c^2\right)=\left(a+b+c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)
Câu a) dễ, ko làm
b) \(x^2y^2+1-x^2-y^2\)
\(=x^2\left(y^2-1\right)-\left(y^2-1\right)\)
\(=\left(x^2-1\right)\left(y^2-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(y+1\right)\left(y-1\right)\)
Câu c) đề sai
Câu c) ,đề đúng nek
\(bc\left(b+c\right)+ac\left(c-a\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left[\left(b+c\right)-\left(a+b\right)\right]-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left(b+c\right)-ac\left(a+b\right)-ab\left(a+b\right)\)
\(=\left(b+c\right)\left(bc+ac\right)-\left(a+b\right)\left(ac+ab\right)\)
\(=\left(b+c\right)c\left(a+b\right)-\left(a+b\right)a\left(b+c\right)\)
\(=\left(b+c\right)\left(a+b\right)\left(c-a\right)\)
a,\(5xy^3-2xyz-15y^2+6z\)
\(=\left(5xy^3-15y^2+6z-2xyz\right)\)
\(=5y^2\left(xy-3\right)-2z\left(xy-3\right)\)
\(=\left(5y^2-2z\right)\left(xy-3\right)\)
a) 5xy3 - 2xyz - 15y2 + 6z
= ( 5xy3 - 15y2 ) - ( 2xyz - 6z )
= 5y2( xy - 3 ) - 2z( xy - 3 )
= ( xy - 3 )( 5y2 - 2z )
b) ab3c2 - a2b2c2 + ab2c3 - a2bc3
= abc2( b2 - ab + bc - ac )
= abc2[ ( b2 - ab ) + ( bc - ac ) ]
= abc2[ b( b - a ) + c( b - a ) ]
= abc2( b - a )( b + c )
biết chết liền
a) \(ab-ac-b^2+bc=\left(ab-ac\right)-\left(b^2-bc\right)\)( Phương pháp nhóm các hạng tử )
\(=a.\left(b-c\right)-b.\left(b-c\right)\) ( Phương pháp đặt nhân tử chung )
\(=\left(a-b\right)\left(b-c\right)\) ( Phương pháp đặt nhân tử chung )
b) \(10a^3-10a=10a.\left(a^2-1\right)=10a.\left(a+1\right)\left(a-1\right)\)
c) \(2a^2xy-18b^2xy=2xy.\left(a^2-9b^2\right)=2xy.\left(a+3y\right)\left(a-3y\right)\)
d) \(\left(a-b\right)\left(a+b\right)+3\left(a+b\right)=\left(a+b\right)\left(a-b+3\right)\)