Question

\(\text{Chứng minh:}\)

\(\left(a^3+a^2b+ab^2+b^3\right)\left(a-b\right)=a^4-b^4\)
 

 

Answer 1

Ta có:  (a³+a²b+ab²+b³)(a-b)=a⁴-b⁴

=> a⁴+a³b+a²b²+ab³-a³b-a²b²-ab³-b⁴=a⁴-b⁴

=> (a³b-a³b)+(a²b²-a²b²)+(ab³-ab³)+(a⁴-b⁴)= a⁴-b⁴

=> a⁴-b⁴=a⁴-b⁴

=>  ĐPCM
 

Answer 2

Xét vế trái

\(\left(a^3+a^2b+ab^2+b^3\right)\left(a-b\right)\)

\(=a^4+a^3b+a^2b^2+ab^3-a^3b-a^2b^2-ab^3-b^4\)

\(=a^4-b^4\)

= vế phải 

=> Đpcm

Answer 3

\(VT=\left(a^3+a^2b+ab^2+b^3\right)\left(a-b\right)\)

\(=a^4-a^3b+a^3b-a^2b^2+a^2b^2-ab^3+b^3a-b^4\)

\(=a^4-b^4=VP\left(đpcm\right)\)

Answer 4

i​ce Wings trình bày sai bét