1) x^2 + 9 -16y^2 + 6x

= (x^2 + 6x+9)-16y^2

= (x+3)^2 - (4y)^2

= (x+3-4y)(x+3+4y)

2) x^2 - 9 + y^2 + 2xy

= (x^2 + 2xy + y^2)-9

= (x+y)^2 - 3^2

= (x+y-3)(x+y+3)

3) x^2 - 4x+4-9y^2

= (x^2-4x+4)-9y^2

= (x-2)^2 - (3y)^2

= (x-2-3y)(x-2+3y)

4) x^2 - 4xy + 4y^2 -81

= (x^2 - 4xy + 4y^2)-81

= (x-2y)^2 - 9^2

= (x-2y-9)(x-2y+9)

5) 25-10x-9y^2 + x^2

= (25-10x+x^2)-9y^2

= (5-x)^2 - (3y)^2

= (5-x-3y)(5-x+3y)

6) 9y^2 - 4x^2 + 4x -1

= 9y^2 - (4x^2 - 4x+1)

= (3y)^2 - (2x-1)^2

= (3y-2x+1)(3y+2x-1)

7) x^2 - 2x - 4y^2 +4y

= ( x^2 - 4y^2 ) - ( 2x + 4y )

= [x^2 - ( 2y )^2 ] - 2( x + 2y )

= ( x - 2y )( x + 2y ) - 2(x + 2y)

= ( x + 2y )(x + 2y - 2 )

8) 64 - 4x^2 + 12xy - 9y^2

= 64 - (4x^2 - 12xy+9y^2)

= 8^2 - (2x-3y)^2

= (8-2x+3y)(8+2x-3y)

1, x^2+9-16x^2+6x

= (x^2+6x+9)-16x^2

=(x+3)^3-(4x)^2

= (x+3-4x)(x+3+4x)

=(3-3x)(5x+3)

2, x^2 -9 +y^2+2xy

= (x^2+2xy+y^2)-3^2

=(x+y)^2-3^2

=(x+y-3)(x+y+3)

3, x^2-4x+4-9y^2

= (x-2)^2 -(3y)^2

=(x-2-3y)(x-2+3y)

4, x^2-4xy+4y^2-81

=(x^-4xy+4y^2)-9^2

=(x-2y)-9^2

=(x-2y-3)(x-2y+3)

5, 25 -10x -9y^2+x^2

= (x^2-10x+25)-(3y)^2

= (x-5-3y)(x-5+3y)

6, 9y^2 -4x^2+4x-1

= (3y)^2-(4x^2-4x+1)

=(3y-2x+1)(3y+2x-1)

7, x^2-2x-4y^2+4y

=x^2-2x-4y^2+4y+1-1

=(x^2-2x+1)-(4y^2-4y+1)

=(x-1)^1-(2y-1)^2

=(x-1-2y+1)(x-1+2y-1)

=(x-2y)(x+2y-2)

8, 64-4x^2+12xy-9y^2

= 8^2-(4x^2-12xy+9y^2)

= 8^2-(2x-3y)^2

=(8-2x+3y)(8+2x-3y)