1. (a+b)²=(a+b)(a+b)=a²+ab+ab+b²=a²+2ab+b² 2. (a-b)²=(a-b)(a-b)=a²-ab-ab+b²=a²-2ab+b²
3. (a+b)³=(a+b)²(a+b)=(a²+2ab+b²)(a+b)=a³+a²b+2a²b+2ab²+ab²+b³=a³+3a²b+3ab²+b³
4. (a-b)³=(a-b)²(a-b)=(a²-2ab+b²)(a-b)=a³-a²b-2a²b+2ab²+ab²-b³=a³-3a²b+3ab²-b³
5. (a+b)(a-b)=a²-ab+ab-b²=a²-b²
6. (a+b)(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³
7. (a-b)(a²+ab+b²)=a³+a²b+ab²-a²b-ab²-b³=a³-b³