Question

[Bẹn's Nguyễn's Hay's Quạo's]

8.Rút gọn biểu thức a) A=(u-v)³+3uv(u+v) b)B=3(c-2d)²+3(c-2d)²+(c+2d)³+(c-2d)³

Answer 1

[Akai Haruma]

Lời giải:
a.

$A=(u-v)^3+3uv(u+v)=u^3-3u^2v+3uv^2-v^3+3u^2v+3uv^2$

$=u^3-v^3+6uv^2$

b.

$3(c-2d)^2+3(c+2d)^2+(c+2d)^3+(c-2d)^3$

$3[(c-2d)^2+(c+2d)^2]+[(c+2d)+(c-2d)][(c+2d)^2-(c+2d)(c-2d)+(c-2d)^2]$

$=3(2c^2+8d^2)+2c[2c^2+8d^2-(c^2-4d^2)]$

$=6(c^2+4d^2)+2c(c^2+12d^2)$

$=2c^3+24cd^2+6c^2+24d^2$