$\displaystyle \begin{array}{{>{\displaystyle}l}} 1) \ 9x^{2} -6xy+y^{2}\\ =( 3x)^{2} -2.3xy+y^{2}\\ =( 3x-y)^{2}\\ 2) \ x^{3} +4x^{2} +4x\\ =x\left( x^{2} +4x+4\right)\\ =x( x+2)^{2}\\ 3) x^{2} -2xy+y^{2} -4z^{2}\\ =( x-y)^{2} -4z^{2}\\ =( x-y-2z)( x-y+2z)\\ 4) \ 5x-5y+ax-ay\\ =5( x-y) +a( x-y)\\ =( 5+a)( x-y)\\ 5) 2x^{2} +3x-5\\ =2x^{2} +5x-2x-5\\ =x( 2x+5) -( 2x+5)\\ =( x-1)( 2x+5)\\ 6) -6x^{2} +7x-2\\ =-6x^{2} +4x+3x-2\\ =-2x( 3x-2) +( 3x-1)\\ =( 1-2x)( 3x-2)\\ 7) \ 5x( x-1) +1-x\\ =5x( x-1) -( x-1)\\ =( x-1)( 5x-1)\\ 8) x^{2} +2x+1-z^{2} +2xz-x^{2}\\ =( x+1)^{2} -( z-x)^{2}\\ =( x+1-z+x)( x+1+z-x)\\ =( 2x+1-z)( 1+z) \ \\ \\ \end{array}$
