Đáp án:+Giải thích các bước giải:

a. $1-8x+16x^2-y^2\\=(1-8x+16x^2)-y^2\\=(1-4x)^2-y^2\\=(1-4x-y)(1-4x+y)\\x^2-2xy+y^2-z^2\\=(x-2xy+y^2)-z^2\\=(x-y)^2-z^2\\=(x-y-z)(x-y+z)\\x^2+4xy-16+4y^2\\=(x^2+4xy+4y^2)-16\\=(x+2y)^2-4^2\\=(x+2y-4)(x+2y+4)\\x^2-16-4xy+4y^2\\=(x^2-4xy+4y^2)-16\\=(x-2y)^2-4^2\\=(x-2y-4)(x-2y+4)$

b. $x^2+3x-x-3\\=(x^2+3x)-(x+3)\\=x(x+3)-(x+3)\\=(x+3)(x-1)\\x^2-y^2+x-y\\=(x^2-y^2)+(x-y)\\=(x-y)(x+y)+(x-y)\\=(x-y)(x+y+1)\\xy+xz+3y+3z\\=(xy+xz)+(3y+3z)\\=x(y+z)+3(y+z)\\=(y+z)(x+3)\\x^2-y^2+5x-5y\\=(x^2-y^2)+(5x-5y)\\=(x-y)(x+y)+5(x-y)\\=(x-y)(x+y+5)$

c. $x^2-3x+2\\=x^2-x-2x+2\\=(x^2-x)-(2x-2)\\=x(x-1)-2(x-1)\\=(x-1)(x-2)\\x^2-5x+6\\=x^2-2x-3x+6\\=(x^2-2x)-(3x-6)\\=x(x-2)-3(x-2)\\=(x-2)(x-3)\\x^2+2x-3\\=x^2-x+3x-3\\=(x^2-x)+(3x-3)\\=x(x-1)+3(x-1)\\=(x-1)(x+3)\\x^2-7x+6\\=x^2-x-6x+6\\=(x^2-x)-(6x-6)\\=x(x-1)-6(x-1)\\=(x-1)(x-6)$

Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.( 2-4x-y)( 1-4x+y) \ \\ b.( x-1)( x+3)\\ c.( x-1)( x-2)\\ a.( x-y-z)( x-y+z)\\ b.( x-y)( x+y+1) \ \\ c.( x-3)( x-2)\\ a.( x+2y-4)( x+2y+4)\\ b.( x+3)( y+z)\\ c.( x-1)( x+3)\\ a.( x-2y-4)( x-2y+4)\\ b.( x-y)( x+y+5)\\ c.( x-1)( x-6) \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ 1-8x+16x^{2} -y^{2} =( 1-4x)^{2} -y^{2}\\ =( 2-4x-y)( 1-4x+y)\\ b.\ x^{2} +3x-x-3=x( x+3) -( x+3)\\ =( x-1)( x+3)\\ c.\ x^{2} -3x+2=x^{2} -2x-x+2\\ =x( x-2) -( x-2)\\ =( x-1)( x-2)\\ a.\ x^{2} -2xy+y^{2} -z^{2}\\ =( x-y)^{2} -z^{2}\\ =( x-y-z)( x-y+z)\\ b.\ x^{2} -y^{2} +x-y\\ =( x-y)( x+y) +( x-y)\\ =( x-y)( x+y+1)\\ c.\ x^{2} -5x+6\\ =x^{2} -2x-3x+6\\ =x( x-2) -3( x-2)\\ =( x-3)( x-2)\\ a.\ x^{2} +4xy-16+4y^{2}\\ =x^{2} +4xy+4y^{2} -4^{2}\\ =( x+2y)^{2} -4^{2}\\ =( x+2y-4)( x+2y+4)\\ b.\ xy+xz+3y+3z\\ =x( y+z) +3( y+z)\\ =( x+3)( y+z)\\ c.\ x^{2} +2x-3\\ =x^{2} +3x-x-3\\ =x( x+3) -( x+3)\\ =( x-1)( x+3)\\ a.\ x^{2} -16-4xy+4y^{2}\\ =x^{2} -4xy+4y^{2} -4^{2}\\ =( x-2y)^{2} -4^{2}\\ =( x-2y-4)( x-2y+4)\\ b.\ x^{2} -y^{2} +5x-5y\\ =( x-y)( x+y) +5( x-y)\\ =( x-y)( x+y+5)\\ c.\ x^{2} -7x+6\\ =x^{2} -6x-x+6\\ =x( x-6) -( x-6)\\ =( x-1)( x-6) \end{array}$