Question

Bài 1. Rút gọn biểu thức:

b) A=(u-v)³+3uv(u+v)

c) C=6(c-d)(c+d)+2(c-d)²-(c-d)³

Bài 2. Tính nhanh:

a) 101³                   b) 299³                  c) 99³

Answer 1

Bài 2.

a) 101³ = (100+1)³ = 100³+3.100².1+3.100.1²+1³ 

   = 1000000+30000+300+1 = 1030301

b) 299³ = (300-1)³ = 300³-3.300².1+3.300.1²-1³

   = 27000000 - 270000 + 900 -1 = 26730899

c) 99³ = (100-1)³ = 100³-3.100².1+3.100.1²-1

   = 1000000 - 30000 + 300 -1 = 970299

Answer 2

\(1,\\ b,A=\left(u-v\right)^3+3uv\left(u+v\right)\\ A=u^3-3u^2v+3uv^2-v^3+3u^2v+3uv^2=u^3-v^3\\ c,6\left(c-d\right)\left(c+d\right)+2\left(c-d\right)^2-\left(c-d\right)^3\\ =6c^2-6d^2+2c^2-4cd+2d^2-c^3+3c^2d-3cd^2+d^3\\ =8c^2-c^3-4d^2-4cd+3c^2d-3cd^2+d^3\)

\(2,\\ a,101^3=\left(100+1\right)^3\\ =100^3+3\cdot10000\cdot1+3\cdot100\cdot1+1\\ =1000000+30000+300+1=1030301\\ b,299^3=\left(300-1\right)^3\\ =300^3-3\cdot90000\cdot1+3\cdot300\cdot1-1\\ =27000000-270000+900-1\\ =26730899\\ c,99^3=\left(100-1\right)^3\\ =100^3-3\cdot10000\cdot1+3\cdot100\cdot1-1\\ =1000000-30000+300-1=970299\)

Answer 3

Bài 1:
a.

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

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

c.

$C=(c-d)[6(c+d)+2(c-d)-(c-d)^2]$

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