$a,(x+2)²-(x+3)(x-3)+10$
$=x²+2x.2+2²-(x²-3²)+10$
$=x²+4x+4-x²+9+10$
$=4x+23$
$b)(x+5)(x²-5x+25)-x(x-4)²+6x$
$=(x³+5³)-x(x²-2.x.4+4²)+6x$
$=x³+125-x(x²-8x+16)+6x$
$=x³+125-x³+8x²-16x+6x$
$=8x²-10x+125$
$c)(x-2y)³-(x+2y)(x²-2xy+4x²)+6x²y$
$=x³-3x².2y+3x.4y²-(2y)³-[x³+(2y)³]+6x²y$
$=x³-6x²y+12xy²-8y³-x³-8y³+6x²y$
$=-16y³+12xy²$