`a)`
`(2x+3y)^2 - (3x-2y)^2`
` = [ (2x)^2 + 2 . 2x . 3y + (3y)^2] - [ (3x)^2 - 2 . 3x . 2y +(2y)^2]`
` = (4x^2 + 12xy + 9y^2) - (9x^2 - 12xy + 4y^2)`
` = 4x^2 + 12xy + 9y^2 - 9x^2 + 12xy - 4y^2`
` = (4x^2 - 9x^2) + (12xy+12xy) + (9y^2 - 4y^2)`
` = -5x^2+ 24xy + 5y^2`
`b)`
`(2a+b)^3 + (4a - 3b)^3 - 2a^3`
` = [ (2a)^3 + 3 . (2a)^2 . b +3 . 2a . b^2 + b^3] + [ (4a)^3 - 3 . (4a)^2 . 3b + 3 . 4a . (3b)^2 - (3b)^3] - 2a^3`
`= (8a^3 + 12a^2b + 6ab^2+ b^3) + (64a^3 - 144a^2b + 108ab^2 - 27a^3) - 2a^3`
` = 8a^3 + 12a^2b + 6ab^2+ b^3 + 64a^3 - 144a^2b + 108ab^2 - 27a^3 - 2a^3`
`= (8a^3 + 64a^3 - 2a^3) + (12a^2b - 144a^2b) + (6ab^2 + 108ab^2) + (b^3 - 27a^3)`
`= 70a^3 -132a^2b + 114ab^2 - 26a^3`
`c)`
`(3x-5)(3x+5) - (6x^2 - 5)^2 - 7x (x^3 + 4)`
` = [ (3x)^2 - 5^2] - [ (6x^2)^2 - 2 . 6x^2 . 5 + 5^2] - (7x . x^3 + 7x . 4)`
` = (9x^2 - 25) - (36x^4 - 60x^2 + 25) - (7x^4 + 28x)`
` = 9x^2 -25 - 36x^4 + 60x^2 - 25 - 7x^4 - 28x`
`= (9x^2 + 60x^2) - (36x^4 + 7x^4) - 28x - (25+25)`
`= 69x^2 - 43x^4 - 28x - 50`
`d)`
`(2x+3)(2x-3) - (2x+1)^2`
`= [(2x)^2 - 3^2] - [ (2x)^2 + 2 . 2x . 1 + 1^2]`
` = (4x^2 - 9) - (4x^2 + 4x + 1)`
`= 4x^2 - 9 - 4x^2 - 4x - 1`
`= -4x- 10`