\(xy^2-9x=x.\left(y^2-3^2\right)=x.\left(y-3\right)\left(y+3\right)\)
\(x^2+14x+49-y^2=\left(x^2+2.7x+7^2\right)-y^2=\left(x+7\right)^2-y^2=\left(x+7-y\right).\left(x+7+y\right)\)
\(xy-y^2-x+y=y.\left(x-y\right)-\left(x-y\right)=\left(x-y\right).\left(y-1\right)\)
\(5x.\left(x-7\right)-x+7=5x.\left(x-7\right)-\left(x-7\right)=\left(x-7\right).\left(5x-1\right)\)
\(x^2-y^2+5x-5y=\left(x-y\right)\left(x+y\right)+5\left(x-y\right)=\left(x-y\right).\left(x+y+5\right)\)
\(5x^3-40=5.\left(x^3-2^3\right)=5.\left(x-2\right).\left(x^2+2x+4\right)\)
\(x^2-y^2+12y-36=\left(y^2-2.6y+6^2-x^2\right)=-\left[\left(y-6\right)^2-x^2\right]\)\(=-\left[y-6-x\right].\left[y-6+x\right]\)
\(x^2z+4xyz+4y^2z=z.\left[x^2+2.2xy+\left(2y\right)^2\right]=z.\left(x+2y\right)^2\)
