Đáp án:
$2)\\ a)(x+y)(x-y-1)\\ b)(x-y-z)(x-y+z)\\ c)(x+y)(x-3)\\ d)(x+3)(z+2y)\\ 3)\\ a)(x-3)(x-4)\\ b)(x-2)(x^2+2x+2)\\ c)(x+1)(x+2)(x+5)$
Giải thích các bước giải:
$2)\\ a)x^2-x-y^2-y\\ =x^2-y^2-x-y\\ =(x-y)(x+y)-(x+y)\\ =(x+y)(x-y-1)\\ b)x^2-2xy+y^2-z^2\\ =(x-y)^2-z^2\\ =(x-y-z)(x-y+z)\\ c)x^2-3x+xy-3y\\ =x^2+xy-3x-3y\\ =x(x+y)-3(x+y)\\ =(x+y)(x-3)\\ d)2xy+3z+6y+xz\\ =xz+3z+2xy+6y\\ =z(x+3)+2y(x+3)\\ =(x+3)(z+2y)\\ 3)\\ a)x^2-7x+12\\ =x^2-3x-4x+12\\ =x(x-3)-4(x-3)\\ =(x-3)(x-4)\\ b)x^3-2x-4\\ =x^3-2x^2+2x^2-4x+2x-4\\ =x^2(x-2)+2x(x-2)+2(x-2)\\ =(x-2)(x^2+2x+2)\\ c)x^3+8x^2+17x+10\\ =x^3+x^2+7x^2+7x+10x+10\\ =x^2(x+1)+7x(x+1)+10(x+1)\\ =(x+1)(x^2+7x+10)\\ =(x+1)(x^2+2x+5x+10)\\ =(x+1)(x(x+2)+5(x+2))\\ =(x+1)(x+2)(x+5)$
