Giải thích các bước giải:

a.Ta có:

$A=x^3-30x^2-31x+1$

$\to A=x^3-(x-1)x^2-x\cdot x+1$ vì $x=31$

$\to A= x^3-x^3+x^2-x^2+1$

$\to A=1$

b.Ta có:

$B=x^5-15x^4+16x^3-29x^2+13x$

$\to B=x^5-(x+5)x^4+(x+6)x^3-(2x-1)x^2+(x+3)x$ vì $x=10$

$\to B=x^5-x^5-5x^4+x^4+6x^3-2x^3+x^2+x^2+3x$

$\to B=-4x^4+4x^3+2x^2+3x$

$\to B=-4\cdot10^4+4\cdot10^3+2\cdot10^2+3\cdot 10$

$\to B=-35770$

c.Ta có:

$C=x(x^2-y)+y(y^2+x)$

$\to C=x^3-xy+y^3+xy$

$\to C=x^3+y^3$

$\to C=(-1)^3+(-1)^3$

$\to C=-2$

d.Ta có:
$D=x^2(x-y)-y(y^2-x^2)$

$\to D=x^2(x-y)-y(y-x)(y+x)$

$\to D=x^2(x-y)-y(y-x)\cdot 0$ vì $x=\dfrac12, y=-\dfrac12$

$\to D=x^2(x-y)$

$\to D=(\dfrac12)^2\cdot (\dfrac12-(-\dfrac12))$

$\to D=\dfrac14$