a. $(3x+4y)^2+(4x-3y)^2-(5x+y)(5x-y)$
$= 9x^2+24xy+16y^2+16x^2-24xy+9y^2-25x^2-y^2$
$= (9x^2+16x^2-25x^2)+(24xy-24xy)+(16y^2+9y^2-y^2)$
$= 24y^2$
b. $(2x+1)^2-2(2x+1)(x+1)+(x+1)^2$
$= (2x+1-x-1)^2$
$= x^2$
c. $(3x+5y)^2+2(3x+5y)(5x-3y)+(5x-3y)^2$
$= (3x+5y+5x-3y)^2$
$= (8x+2y)^2$
$= 64x^2+32xy+4y^2$
d. $(2x-7y)^2+2(2x-7y)(8y-9x)+(9x-8y)^2$
$= (2x-7y)^2+2(2x-7y)(8y-9x)+(8y-9x)^2$
$= (2x-7y+8y-9x)^2$
$= (-7x+y)^2$
$= 49x^2-14xy+y^2$