Question

Sa se arate ca pentru oricare a,b e(apartine)  R avem :
1. (a+b)^2 = a^2 + 2ab +b^2.
2 (a-b)^2 = a^ - 2ab +b^2.
3. a^2 - b^2 = (a-b) ( a+b).
4.(a-b)^3 = a^3 - b^3 - 3ab ( a-b).   Va rog sa ma ajutati, am mare nevoie!

Answer 1

1.(a+b)^2=(a+b)(a+b)=a^2+ab+ab+b^2=a^2+2ab+b^2
2.(a-b)^2=(a-b)(a-b)=a^2-ab-ab+b^2=a^2-2ab+b^2
3.(a-b)(a+b)=a^2+ab-ab-b^2=a^2-b^2
4.(a-b)^3=(a-b)^2*(a-b)=(a^2-2ab+b^2)(a-b)=a^3-2a^2b+b^2a-a^2b+2b^2a-b^3=a^3-3ab(a-b)-b^3