\(16x-5x^2-3\)
\(=-\left(5x^2-16x+3\right)\)
\(=-\left[5x\left(x-\dfrac{1}{5}\right)-15\left(x-\dfrac{1}{5}\right)\right]\)
\(=-5\left(x-3\right)\left(x-\dfrac{1}{5}\right)\)
\(\left(xy+1\right)^2-x^2-2xy-y^2\)
\(=x^2y^2+2xy+1-x^2-2xy-y^2\)
\(=\left(x^2y^2-y^2\right)-\left(x^2-1\right)\)
\(=y^2\left(x^2-1\right)-\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(y-1\right)\left(y+1\right).\)
16x - 5x2 - 3 = -5x2 + 15x + x - 3= 5x(3 -x) - (3 - x)
= ( 3 - x )(5x - 1)
(xy + 1)2 - x2 - 2xy - y2 = (xy + 1)2 -( x2 + 2xy + y2)
= (xy + 1)2 - (x + y )2
= (xy+ 1 - x - y) (xy + 1 + x + y)
=[(xy - x) - (y - 1)][(xy+x) +(y + 1)]
= [x (y - 1) - (y - 1)][x ( y + 1 ) +(y + 1)]
= (y-1) (x- 1) (y+1)(x+1)
