Question

Cum demonstrez formula a^5-b^5

Answer 1

Poti sa faci asa:
a^2-b^2=(a+b)(a-b)
a^3-b^3=(a-b)(a^2+ab+b^)
a^4-b^4=(a-b)(a^3+a^2b+ab^2+b^2)
a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)

Prin urmare, se observa ca a^n-b^n=(a-b)[a^(n-1)b+a^(n-2)b^2+a^(n-3)b^3+.....+ab^(n-1)]. Aceasta este formula binomului general.