$\text{Đáp án+Giải thích các bước giải:}$
$a) (x+y-z)²-4y²=(x+y-z+2z)(x+y-z-2z)=(x+y+z)(x+y-3z)$
$b) (x+1)³-2.(1-x)²=x³+3x²+3x+1-2(1-2x+x²)$
$= x³+3x²+3x+1-2+4x-2x²=x³+x²+7x-1$
$c) (x+y)(x²-xy+y²)-2x³-2y³=x³+y³-2x³-2y³=-x³-y³$
d) (x+ $\dfrac{y}{2}$ ) ² - (y+ $\dfrac{x}{2}$ ) ² $+(x+y+1)²$
= (x+$\dfrac{y}{2}$-y-$\dfrac{x}{2}$)(x+ $\dfrac{y}{2}$+y+ $\dfrac{x}{2}$ ) $+ (x+y+1)²$
= $\dfrac{3(x²-y²)}{2}$ $+x²+y²+1+2xy+2x+2y=2x²+2xy+$ $\dfrac{y}{4}$ $+2x+2y+1-$ $\dfrac{x}{4}$