Bài `1,`
\(a,x^2-6x\\ =x\left(x-6\right)\\ b,4x-6xy\\ =2x\left(2-3y\right)\\ c,2\left(x+5\right)-5x\left(x+5\right)\\ =\left(x+5\right)\left(2-5x\right)\\ d,2\left(x+y\right)-5y\left(x+y\right)\\ =\left(x+y\right)\left(2-5y\right)\)
Bài `2,`
\(a,\left(x-1\right)^2-\left(x-1\right)\\ =\left(x-1\right)\left(x-1\right)-\left(x-1\right)\\ =\left(x-1\right)\left(x-1-1\right)\\ =\left(x-1\right)\left(x-2\right)\\ b,x\left(x+2\right)+y\left(x+2\right)\\ =\left(x+2\right)\left(x+y\right)\\ c,xy\left(x-y\right)-2x+2y\\ =xy\left(x-y\right)-\left(2x-2y\right)\\ =xy\left(x-y\right)-2\left(x-y\right)\\ =\left(x-y\right)\left(xy-2\right)\)
\(d,3\left(x-y\right)+2y\left(y-x\right)\\ =3\left(x-y\right)-2y\left(x-y\right)\\ =\left(x-y\right)\left(3+2y\right)\\ e,6\left(2x-y\right)-3\left(y-2x\right)\\ =6\left(2x-y\right)+3\left(2x-y\right)\\ =\left(2x-y\right)9\\ e,\left(3x-2y\right)^2+\left(3x-2y\right)\\ =\left(3x-2y\right)\left(3x-2y\right)+\left(3x-2y\right)\\ =\left(3x-2y\right)\left(3x-2y+1\right)\)
Bài `3`
\(a,xy-z+y-xz\\ =\left(xy+y\right)-\left(z+xz\right)\\ =y\left(x+1\right)-z\left(1+x\right)\\ =\left(x+1\right)\left(y-z\right)\)
`b, x^2 -bx+ax-ab`
`=x(x-b)+a(x-b)`
`=(x-b)(x+a)`
`d, x^3 -4x^2 -9x+36`
`=(x^3 -9x)-(4x^2 -36)`
`= x(x^2 -9) - 4(x^2-9)`
`=(x^2-9)(x-4)`
`=(x-3)(x+3)(x-4)`
`e, x^3 +2x^2 +2x+1`
`=x^3 +x^2+x^2+x+x+1`
`=(x^3+x^2+x)+(x^2+x+1)`
`= x(x^2 +x+1)+(x^2+x+1)`
`=(x^2+x+1)(x+1)`
`g, x^2 -2x-4y^2-4y`
`=x^2 -2x-(2y)^2 -4y`
`=[x^2 -(2y)^2] -(2x+4y)`
`=(x-2y)(x+2y)-2(x+2y)`
`=(x+2y)(x-2y-2)`
Bài 3
1) xy - z + y - xz
= (xy - xz) + (y - z)
= x(y - z) + (y - z)
= (y - z)(x + 1)
2) x² - bx + ax - ab
= (x² - bx) + (ax - ab)
= x(x - b) + a(x - b)
= (x - b)(x + a)
3) a⁴ + a³ + a² + a
= (a⁴ + a³) + (a² + a)
= a³(a + 1) + a(a + 1)
= (a + 1)(a³ + a)
= a(a + 1)(a² + 1)
4) x³ - 4x² - 9x + 36
= (x³ - 4x²) - (9x - 36)
= x²(x - 4) - 9(x - 4)
= (x - 4)(x² - 9)
= (x - 4)(x - 3)(x + 3)
5) x³ + 2x² + 2x + 1
= (x³ + x²) + (x² + 2x + 1)
= x²(x + 1) + (x + 1)²
= (x + 1)(x² + x + 1)
6) x² - 2x - 4y² - 4y
= x² - 2x + 1 - 4y² - 4y - 1
= (x² - 2x + 1) - (4y² + 4y + 1)
= (x - 1)² - (2y + 1)²
= (x - 1 - 2y - 1)(x - 1 + 2y + 1)
= (x - 2y - 2)(x + 2y)
