二项式公式
| (a + b)2 = a2 + 2ab + b2 | 平方的和 |
| (a – b)2 = a2 – 2ab + b2 | 平方的差 |
| a2 – b2 = (a – b)(a + b) | 差的平方 |
| (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc | |
三项式公式
| (a + b)3 = a3 + 3a2b + 3ab2 + b3 | 立方的和 |
| (a – b)3 = a3 – 3a2b + 3ab2 – b3 | 立方差 |
| a3 + b3 = (a + b)(a2 – ab + b2) | 和的立方 |
| a3 – b3 = (a – b)(a2 + ab + b2) | 差立方 |
四项式公式
| (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 |
| (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4 |
| a4 – b4 = (a – b)(a + b)(a2 + b2) |
二项式定理
| (a + b)n = an + nan – 1b + n(n – 1)2an – 2b2 + ... + n!k!(n – k)!an – kbk + ... + bn |
| (a - b)n = an - nan – 1b + n(n – 1)2an – 2b2 + ... + (-1)kn!k!(n – k)!an – kbk + ... + (-1)nbn |
