a. (8x+2√3y)²=(8x)²+2*8x*2√3y+(2√3y)²=64x²+32√3xy+12y²
b. √8=√2³=2√2
(7x-√8y²)²=(7x)²-2*7x*√8y²+(√8y²)²=49x²-14x*2√2y²+8y^{4} =
=49x²-28√2xy²+8y^{4}
c. (8x-20)(8x+20)=(8x)²-20²=64x²-400
d. 100x²-144=(10x)²-12²=(10x-12)*(10x+12)
e. (x-√5)(x+√5)-(x+2)²=x²-(√5)²-(x²+2*x*2+2²)=x²-5-x²+4x-4=4x-9
f. (√5x+3)²-(2√5x-√3)(2√5x+√3)+(3√6x-1)²=
=(√5)²+2*√5*3+3²-[(2√5)²-(√3)²]+(3√6)²-2*3√6*1+1²=
=5+6√5+9-(4*5-3)+9*6-6√6+1=
=14+6√5-17+55-6√6=
=52+6√5-6√6
g. (3-√2x)²+(√6+√3x)²-(√15-√2x)(√15+√2x)=
=3²-2*3*√2x+(√2x)²+(√6)²+2*√6*√3x+(√3x)²-[(√15)²-(√2x)²]=
=9-6√2x+2x²+6+2√(6*3)x+3x²-(15-2x²)=
=5x²-6√2x+6√2x+15-15+2x²=
=7x²
