\(1) \ 5(x - y) - y(x - y) = (x - y)(5 - y)\)
\(2) \ x(y + 1) + 8(y + 1) = (y + 1)(x + 8)\)
\(3) \ 5(x - y) - x(x - y) = (x - y)(5 - x)\)
\(4) \ z(x + y) - 5(x + y) = (x + y)(z - 5)\)
\(5) \ 3x(x + 5) - 2(5 + x) = (x + 5)(3x - 2)\)
\(6) \ x^2(x - 1) + 4(x - 1) = (x - 1)(x^2 + 4)\)
\(7) \ 5x(x - 1) - (1 - x) = 5x(x - 1) + (x - 1) = (x - 1)(5x + 1)\)
\(8) \ x(y - 1) - y(1 - y) = x(y - 1) + y(y - 1) = (y - 1)(x + y)\)
\(9) \ y(x - 2) - 3(2 - x) = y(x - 2) + 3(x - 2) = (x - 2)(y + 3)\)
\(10) \ 3(x - y) - y(y - x) = 3(x - y) + y(x - y) = (x - y)(3 + y)\)
\(11) \ 3x(x - 2) + 5(2 - x) = 3x(x - 2) - 5(x - 2) = (x - 2)(3x - 5)\)
\(12) \ 7x(x - y) - (y - x) = 7x(x - y) + (x - y) = (x - y)(7x + 1)\)
\(13) \ 3x(x - 1) - 2y(1 - x) = 3x(x - 1) + 2y(x - 1) = (x - 1)(3x + 2y)\)
\(14) \ 3(x - y) - 5x(y - x) = 3(x - y) + 5x(x - y) = (x - y)(3 + 5x)\)
\(15) \ x(x - y) + y(y - x) = x(x - y) - y(x - y) = (x - y)(x - y) = (x - y)^2\)
\(16)\ x(y^2-1)+4(1-y^2)=x(y^2-1)-4(y^2-1)\)
\(=(y^2-1)(x-4)=(y-1)(y+1)(x-4)\)
\(17) \ x(2y - 1) - 5(2y - 1) = (2y - 1)(x - 5)\)
\(18) \ 9(x - 2y) + x(2y - x) = 9(x - 2y) - x(x - 2y) = (x - 2y)(9 - x)\)
\(19) \ 10x(x - y) - 8y(y - x) = 10x(x - y) + 8y(x - y) = 2(x - y)(5x + 4y)\)
\(20) \ 3x(x - y) + 6(y - x) = 3x(x - y) - 6(x - y) = 3(x - y)(x - 2)\)
\(21) \ 5x(x - 1) - 15x(1 - x) = 5x(x - 1) + 15x(x - 1) = 20x(x - 1)\)
\(22) \ 10x(x - y) - 6y(y - x) = 10x(x - y) + 6y(x - y) = 2(x - y)(5x + 3y)\)
\(23)\ 3x(x-2y)+6y(2y-x)=3x(x-2y)-6y(x-2y)\)
\(=3(x-2y)(x-2y)=3(x-2y)^2\)
\(24) \ 20x(x + y) - 8y(y + x) = 4(x + y)(5x - 2y)\)
\(25)\ xy^2(x-3)+4x(3-x)=xy^2(x-3)-4x(x-3)\)
\(=x(x-3)(y^2-4)=x(x-3)(y-2)(y+2)\)
\(26) \ 2x(x + y) - 6x^2(x + y) = 2x(x + y)(1 - 3x)\)
\(27) \ 9x^2(y + z) + 3x(y + z) = 3x(y + z)(3x + 1)\)
\(28) \ 2x^2(y - 1) - 2x(y - 1) = 2x(y - 1)(x - 1)\)
\(29)\ 10xy(x-y)-6y(y-x)\)
\(=10xy(x-y)+6y(x-y)=2y(x-y)(5x+3)\)
1: 5(x-y)-y(x-y)
=(x-y)(5-y)
2: x(y+1)+8(y+1)=(x+8)(y+1)
3: 5(x-y)-x(x-y)
=(x-y)(5-x)
4: z(x+y)-5(x+y)
=(x+y)(z-5)
5: 3x(x+5)-2(5+x)
=3x(x+5)-2(x+5)
=(x+5)(3x-2)
6: \(x^2\left(x-1\right)+4\left(x-1\right)=\left(x-1\right)\left(x^2+4\right)\)
7: 5x(x-1)-(1-x)
=5x(x-1)+(x-1)
=(x-1)(5x+1)
8: x(y-1)-y(1-y)
=x(y-1)+y(y-1)
=(y-1)(x+y)
9: y(x-2)-3(2-x)
=y(x-2)+3(x-2)
=(x-2)(y+3)
10: 3(x-y)-y(y-x)
=3(x-y)+y(x-y)
=(x-y)(y+3)
11: 3x(x-2)+5(2-x)
=3x(x-2)-5(x-2)
=(x-2)(3x-5)
12: 7x(x-y)-(y-x)
=7x(x-y)+(x-y)
=(x-y)(7x+1)
13: \(3x\left(x-1\right)-2y\left(1-x\right)\)
=3x(x-1)+2y(x-1)
=(x-1)(3x+2y)
14: 3(x-y)-5x(y-x)
=3(x-y)+5x(x-y)
=(x-y)(5x+3)
15: x(x-y)+y(y-x)
=x(x-y)-y(x-y)
=(x-y)(x-y)
\(=\left(x-y\right)^2\)
16: \(x\left(y^2-1\right)+4\left(1-y^2\right)=x\left(y^2-1\right)-4\left(y^2-1\right)\)
\(=\left(x-4\right)\left(y^2-1\right)=\left(x-4\right)\left(y-1\right)\left(y+1\right)\)
17: x(2y-1)-5(2y-1)=(2y-1)(x-5)
18: 9(x-2y)+x(2y-x)
=9(x-2y)-x(x-2y)
=(x-2y)(9-x)
19: 10x(x-y)-8y(y-x)
=10x(x-y)+8y(x-y)
=(x-y)(10x+8y)
=2(5x+4y)(x-y)
20: 3x(x-y)+6(y-x)
=3x(x-y)-6(x-y)
=(x-y)(3x-6)
=3(x-2)(x-y)
21: 5x(x-1)-15x(1-x)
=5x(x-1)+15x(x-1)
=20x(x-1)
22: 10x(x-y)-6y(y-x)
=10x(x-y)+6y(x-y)
=(x-y)(10x+6y)
=2(5x+3y)(x-y)
23: 3x(x-2y)+6y(2y-x)
=(3x-6y)(x-2y)
\(=3\left(x-2y\right)^2\)
24: 20x(x+y)-8y(y+x)
=20x(x+y)-8y(x+y)
=(x+y)(20x-8y)
=4(5x-2y)(x+y)
25: \(xy^2\left(x-3\right)+4x\left(3-x\right)=\left(x-3\right)\left(xy^2-4x\right)\)
\(=x\left(x-3\right)\cdot\left(y^2-4\right)\)
=x(x-3)(y-2)(y+2)
26: \(2x\left(x+y\right)-6x^2\left(x+y\right)\)
\(=\left(x+y\right)\left(2x-6x^2\right)\)
\(=2x\left(1-3x\right)\left(x+y\right)\)
27: \(9x^2\left(y+z\right)+3x\left(y+z\right)\)
\(=\left(y+z\right)\left(9x^2+3x\right)\)
=3x(3x+1)(y+z)
28: \(2x^2\left(y-1\right)-2x\left(y-1\right)\)
\(=\left(y-1\right)\left(2x^2-2x\right)\)
=2x(x-1)(y-1)
29: \(10xy\left(x-y\right)-6y\left(y-x\right)\)
=10xy(x-y)+6y(x-y)
=(x-y)(10xy+6y)
=2y(5x+3)(x-y)
1. 5(x - y) - y(x - y) Có nhân tử chung là (x - y) nên ta đặt ra ngoài: = (x - y)(5 - y) 2. x(y + 1) + 8(y + 1) Có nhân tử chung là (y + 1) nên ta đặt ra ngoài: = (y + 1)(x + 8) 3. 5(x - y) - x(x - y) Có nhân tử chung là (x - y) nên ta đặt ra ngoài: = (x - y)(5 - x) 4. z(x + y) - 5(x + y) Có nhân tử chung là (x + y) nên ta đặt ra ngoài: = (x + y)(z - 5)
