`a)`
`(3x-1)^2 - 16`
`= (3x-1)^2 -4^2`
`= (3x-1-4)(3x-1+4)`
` = (3x-5)(3x+3)`
`= (3x-5) . 3 . (x+1)`
`b)`
`(5x-4)^2 - 49x^2`
` = (5x-4)^2 - (7x)^2`
` = (5x - 4 - 7x)(5x-4 + 7x)`
` = (-2x-4)(12x-4)`
`= -2 (x+2) . 4 . (3x-1)`
`= - 8 (x+2)(3x-1)`
`c)`
`(2x+5)^2 - (x-9)^2`
`= [ (2x+5) - (x-9)] . [ (2x+5) + (x-9)]`
`= (2x + 5 - x + 9)(2x+5 + x-9)`
` = (x+14)(3x-4)`
`d)`
`(3x+1)^2 - 4(x-2)^2`
` = (3x+1)^2 - [ 2 (x-2)]^2`
` = (3x+1)- (2x -4)^2`
`= [(3x+1) - (2x-4)] . [ (3x+1) + (2x-4)]`
`= (3x + 1 - 2x+4)(3x+1 + 2x-4)`
` = (x +5)(5x-3)`
`e)`
`9 (2x+3)^2 - 4(x+1)^2`
`= [ 3 (2x+3)]^2 - [ 2 (x+1)]^2`
` = (6x + 9)^2 - (2x + 2)^2`
` = [ (6x+9) - (2x+2)] . [ (6x+9) + (2x+2)]`
` = (6x + 9 - 2x - 2)(6x+9+2x+2)`
` = (4x + 7)(8x + 11)`
`f)`
`4 b^2 c^2 - (b^2 + c^2 - a^2)^2`
`= (2bc)^2 - (b^2 + c^2 - a^2)^2`
`= [ 2bc - (b^2 + c^2 - a^2)] . [ 2bc + (b^2 + c^2 -a^2)]`
` = (2abc - b^2 - c^2 + a^2) . (2bc + b^2 +c^2 - a^2)`
` = (2abc - b^2 - c^2 + a^2) . [ (b^2 + c^2 - 2abc) - a^2]`
` = (2abc - b^2 - c^2 + a^2) . [ (b+c)^2- a^2]`
` = (2abc - b^2 - c^2 + a^2) . (b + c -a)(b+c+a)`
