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x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz
=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2
=xy(x+y+z)+zx(x+y+z)+yz(y+z)
=x(y+z)(x+y+z)+yz(y+z)
=(y+z)(x^2+xy+zx+yz)
=(x+y)(y+z)(z+x)
t i c k mk nha!!! 565464556756768768787669789789776575656767676945645645654
a, \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)\(=x^2y+xy^2+y^2z+yz^2+x^2z+xz^2+2xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z\right)\)
\(=x\left(x+y+z\right)\left(y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+z\right)+y\left(x+z\right)\right]\)
\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)
b, \(2x^2+2y^2-x^2z+z-y^2z-2\)
\(=\left(2x^2-x^2z\right)+\left(2y^2-y^2z\right)-\left(2-z\right)\)
\(=x^2\left(2-z\right)+y^2\left(2-z\right)-\left(2-z\right)\)
\(=\left(2-z\right)\left(x^2+y^2-1\right)\)
1) \(4x^2-7x-2=4x^2-8x+x-2=\left(4x^2-8x\right)+\left(x-2\right)\)
\(=4x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(4x+1\right)\)
2) \(4x^2+5x-6=4x^2+8x-3x-6=\left(4x^2+8x\right)-\left(3x+6\right)\)
\(=4x\left(x+2\right)-3\left(x+2\right)=\left(x+2\right)\left(4x-3\right)\)
3) \(5x^2-18x-8=5x^2-20x+2x-8=\left(5x^2-20x\right)+\left(2x-8\right)\)
\(=5x\left(x-4\right)+2\left(x-4\right)=\left(x-4\right)\left(5x+2\right)\)
4) \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)
\(=xy\left(x+y\right)-y^2z-yz^2+x^2z-xz^2\)
\(=xy\left(x+y\right)+\left(x^2z-y^2z\right)-\left(yz^2+xz^2\right)\)
\(=xy\left(x+y\right)+z\left(x^2-y^2\right)-z^2.\left(x+y\right)\)
\(=xy\left(x+y\right)+z\left(x-y\right)\left(x+y\right)-z^2\left(x+y\right)\)
\(=xy\left(x+y\right)+\left(zx-zy\right)\left(x+y\right)-z^2\left(x+y\right)\)
\(=\left(x+y\right)\left(xy+xz-yz-z^2\right)=\left(x+y\right).\left[x\left(y+z\right)-z\left(y+z\right)\right]\)
\(=\left(x+y\right)\left(y+z\right)\left(x-z\right)\)
1) 4x2 - 7x - 2 = 4x2 - 8x + x - 2 = 4x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 4x + 1 )
2) 4x2 + 5x - 6 = 4x2 - 8x + 3x - 6 = 4x( x - 2 ) + 3( x - 2 ) = ( x - 2 )( 4x + 3 )
3) 5x2 - 18x - 8 = 5x2 - 20x + 2x - 8 = 5x( x - 4 ) + 2( x - 4 ) = ( x - 4 )( 5x + 2 )
4) xy( x + y ) - yz( y + z ) + xz( x - z )
= x2y + xy2 - y2z - yz2 + xz( x - z )
= ( x2y - yz2 ) + ( xy2 - y2z ) + xz( x - z )
= y( x2 - z2 ) + y2( x - z ) + xz( x - z )
= y( x - z )( x + z ) + y2( x - z ) + xz( x - z )
= ( x - z )[ y( x + z ) + y2 + xz ]
= ( x - z )( xy + yz + y2 + xz )
= ( x - z )[ ( xy + y2 ) + ( xz + yz ) ]
= ( x - z )[ y( x + y ) + z( x + y ) ]
= ( x - z )( x + y )( y + z )
5) xy( x + y ) + yz + xz( x + z ) + 2xyz ( đề có thiếu không vậy .-. )
a)=x2-5x-2x+10=x(x-5)-2(x-5)=(x-5)(x-2)
b)=4x2-4x+x-1=4x(x-1)+(x-1)=(x-1)(4x+1)
c)=x2-4x+3x-12=x(x-4)+3(x-4)=(x-4)(x+3)
1) \(x^2-x-y^2-y=\left(x^2-y^2\right)-\left(x+y\right)=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)
\(x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
2)\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(a+5\right)\)
\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)
6,
=a4 [-(a-b)-(c-a)] + [b4(c-a)+c4(a-b)]
=rồi nhóm hạng tử chung lại
=và sau đó tách ra bằng hằng đẳng thức
kết quả =(a-b)(c-a)(c-b)(a2+b2+c2+ab+bc+ca)
Bài này khá dài nên mk nhác viết , bn cố gắng làm bài nhé !
x2 + 5x + 6
= x2 + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2)(x + 3)
7x - 6x2 - 2
= - 6x2 + 7x - 2
= - 6x2 + 3x + 4x - 2
= - 3x(2x - 1) + 2(2x - 1)
= (2x - 1)(-3x + 2)
mk ko pit lm câu a, xl nhé
\(\text{a) }xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\\ \\=x^2y+xy^2+y^2z+yz^2+x^2z+xz^2+xyz+xyz\\ \\=\left(x^2y+xy^2+x^2z+xyz\right)+\left(xz^2+yz^2+y^2z+xyz\right)\\ \\=x\left(xy+y^2+xz+yz\right)+z\left(xz+yz+y^2+xy\right)\\ \\=\left(x+z\right)\left(xy+y^2+xz+yz\right)\\ =\left(x+z\right)\left[\left(xy+y^2\right)+\left(xz+yz\right)\right]\\=\left(x+z\right)\left[y\left(x+y\right)+z\left(x+y\right)\right]\\ \\=\left(x+z\right)\left(y+z\right)\left(x=y\right) \)
\(\text{b) }x^2+5x+6\\ \\ =x^2+2x+3x+6\\ \\=\left(x^2+2x\right)+\left(3x+6\right)\\ \\=x\left(x+2\right)+3\left(x+2\right)\\ \\=\left(x+2\right)\left(x+3\right)\)
\(\text{c) }7x-6x^2-2\\ \\ =3x+4x-6x^2-2\\ \\ =\left(3x-6x^2\right)-\left(2-4x\right)\\ \\ =3x\left(1-2x\right)+2\left(1-2x\right)\\ \\ =\left(3x+2\right)\left(1-2x\right)\)