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a) \(x\left(x-y\right)+x-y\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
b) \(2x+2y-x\left(x+y\right)\)
\(=2\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(2-x\right)\)
c) \(5x^2-5xy-10x+10y\)
\(=5x\left(x-y\right)-10\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-10\right)\)
d) \(4x^2+8xy-3x-6y\)
\(=4x\left(x+2y\right)-3\left(x+2y\right)\)
\(=\left(x+2y\right)\left(4x-3\right)\)
e) \(2x^2+2y^2-x^2z+z-y^2z-2\)
\(=\left(2x^2+2y^2-2\right)-\left(x^2z-z+y^2z\right)\)
\(=2\left(x^2+y^2-1\right)-z\left(x^2-1+y^2\right)\)
\(=\left(x^2+y^2-1\right)\left(2-z\right)\)
a) \(2x-6y=2\left(x-3y\right)\)
b) \(x^2-y^2=\left(x-y\right)\left(x+y\right)\)
c) \(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)
d) \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
e) \(x^3-10x^2+25x=x\left(x^2-10x+25\right)=x\left(x-5\right)^2\)
f) \(xy+y^2-x-y=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)
a. 2x - 6y
Bài làm
a. 2x - 6y
= 2(x - 3y)
b. x2 - y2
= (x - y)(x + y)
c. 2x3 + 4x2 + 2x
= 2x(x2 + 2 + 1)
= 2x(x2 + 3)
d. x2 - 2xy + y2 - 9
= (x2 - 2xy + y2) - 9
= (x - y)2 - 9
= (x - y - 3)(x - y + 3)
e. x3 - 10x2 + 25x
= x(x2 - 10x + 25)
= x(x2 - 2.5.x + 52)
= x(x + 5)2
f. xy + y2 - x - y
= y(x + y) - (x + y)
= (x + y)(y - 1)
a) 2x - 6y = 2( x - 3y )
b) x2 - y2 = ( x - y )( x + y )
c) 2x3 + 4x2 + 2x = 2x( x2 + 2x + 1 ) = 2x( x + 1 )2
d) x2 - 2xy + y2 = ( x2 - 2xy + y2 ) - 9 = ( x - y )2 - 32 = ( x - y - 3 )( x - y + 3 )
e) x3 - 10x2 + 25x = x( x2 - 10x + 25 ) = x( x - 5 )2
f) xy + y2 - x - y = ( xy + y2 ) - ( x + y ) = y( x + y ) - ( x + y ) = ( x + y )( y - 1 )
a) \(6x^3-12x^2y^2+6xy^3=6x.\left(x^2-2xy^2+y^3\right)\)
b) \(\left(x^2+4\right)^2-16=\left(x^2+4-4\right)\left(x^2+4+4\right)=x^2\left(x^2+8\right)\)
c) \(5x^2-5xy-10x+10y=\left(5x^2-5xy\right)-\left(10x-10y\right)=5x\left(x-y\right)-10\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-10\right)=5\left(x-y\right)\left(x-2\right)\)
d) \(a^3-3a+3b-b^3=\left(a^3-b^3\right)-\left(3a-3b\right)=\left(a-b\right)\left(a^2+ab+b^2\right)-3.\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2+ab+b^2-3\right)\)
e) \(x^2-2x-y^2+1=\left(x^2-2x+1\right)-y^2=\left(x-1\right)^2-y^2=\left(x-1-y\right)\left(x-1+y\right)\)
f) \(x^2-x-2=x^2+x-2x-2=\left(x^2+x\right)-\left(2x+2\right)=x\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(x-2\right)\)
g) \(x^4-5x^2+4=x^4-4x^2+4-x^2=\left(x^4-4x^2+4\right)-x^2=\left(x^2-2\right)^2-x^2\)
\(=\left(x^2-2-x\right)\left(x^2-2+x\right)\)
j) \(x^3-x^3-2x^2-x=-2x^2-x=-\left(2x^2+x\right)=-x\left(2x+1\right)\)
k) \(\left(a^3-27\right)-\left(3-a\right)\left(6a+9\right)=\left(a-3\right).\left(a^2+3a+9\right)+\left(a-3\right)\left(6a+9\right)\)
\(\left(a-3\right)\left(a^2+3a+9+6a+9\right)=\left(a-3\right)\left(a^2+9a+18\right)\)
h) \(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)
\(=x^2y-x^2z+y^2z-y^2x+z^2x-z^2y\)
\(=\left(x^2y-y^2x\right)-\left(x^2z-y^2z\right)+\left(z^2x-z^2y\right)\)
\(=xy\left(x-y\right)-z\left(x^2-y^2\right)+z^2\left(x-y\right)\)
\(=xy\left(x-y\right)-z\left(x-y\right)\left(x+y\right)+z^2\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-zx-zy+z^2\right)\)
\(=\left(x-y\right)\left[\left(xy-zx\right)-\left(zy-z^2\right)\right]\)
\(=\left(x-y\right)\left[x\left(y-z\right)-z\left(y-z\right)\right]\)
\(\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
cái này cách tốt nhất là vào Cốc Cốc Math rồi gõ các nhân tử vào là nó sẽ ra nhé !
^_^
\(2x^4-9x^3+2x^3-9x^2+7x^2+7x+6x+6\)
\(\left(2x^4+2x^3\right)-\left(9x^3+9x^2\right)+\left(7x^2+7x\right)+\left(6x+6\right)\)
\(2x^3\left(x+1\right)-9x^2\left(x+1\right)+7x\left(x+1\right)+6\left(x+1\right)\)
\(\left(x+1\right)\left(2x^3-9x^2+7x+6\right)\)
b)\(\left(10x^4-50x^3y\right)+\left(23x^3y-115x^2y^2\right)+\left(5x^2y^2-25xy^3\right)-\left(2xy^3-10y^4\right)\)
\(10x^3\left(x-5y\right)+23x^2y\left(x-5y\right)+5xy^2\left(x-5y\right)-2y^3\left(x-5\right)\)
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, \(2x^2+2y^2-x^2z+z-y^2z-2\)
\(=\left(2x^2-x^2z\right)+\left(2y^2-y^2z\right)-\left(2-z\right)\)
\(=x^2\left(2-z\right)+y^2\left(2-z\right)-\left(2-z\right)\)
\(=\left(2-z\right)\left(x^2+y^2-1\right)\)
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 )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
a) \(x^2+2x+1-y^2 = (x^2 +2x+1) – y^2\)
\(= (x+1)^2 - y^2\)
\(= (x+1+ y) (x+1- y)\)
b) \(2xy+z+2x+yz\)
\(=\left(2xy+2x\right)+\left(z+yz\right)\)
\(=2x\left(y+1\right)+z\left(y+1\right)\)
\(=\left(2x+z\right)\left(y+1\right)\)
c) \(x^2+x-xy-y\)
\(=\left(x^2+x\right)-\left(xy+y\right)\)
\(=x\left(x+1\right)-y\left(x+1\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
d) \(5x^2-5xy+10x+10y\)
\(=\left(5x^2-5xy\right)+\left(10x+10y\right)\)
\(=5x\left(x-y\right)-10\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-10\right)\)
a, x2+2x+1-y2= (x+1)2-y2= (x+1-y)(x+1+y)
b, 2xy+z+2x+yz= (2xy+2x)+(z+yz)
= 2x(y+1)+z(y+1)
= (2x+z)(y+1)
c, x2 +x - xy - y = x(x+1) - y(x+1)
= (x - y)(x+1)
d, 5x2 - 5xy - 10x + 10y=5x(x-y) - 10(x-y)
= (5x-10)(x-y).(Câu này có thể là sai đề nên mik đã sửa lại đề cho dễ làm nha). Chúc bạn học tốt!!!