The binomial theorem, also known as Newton's binomial theorem, gives the integer power of the sum of two numbers, such as the sum of similar terms. The binomial theorem discusses the expansion of (a+b) n, and the following formula can be obtained:

1 、( a+b)2=a2+2ab+b2

2 、( a+b)3=a3+3a2b+3ab2+b3

3 、( a+b)4=a4+4a3b+6a2b2+4ab3+b4？

The binomial theorem was originally used to open higher powers. In China, Nine Chapters Arithmetic, written in 1 century AD, put forward the world's earliest general program for finding the square root and square root of multiple positive integers. 165438+In the middle of the 20th century, Jia Xian gave the "Original Drawing of Rooting Method" in his book "Calculation of Unlocking", which met the needs of more than three times.

Extended data

1. If the binomial is in the form of ax+b (where A and B are constants and X is a variable), then the binomial is linear.

2. In Arabia, in the10th century, Al Karadji had known the construction method of binomial coefficient table: any number in each column is equal to the number in the same row in the previous column plus the number above it. 11~12nd century, Omar Hagham extended Indian roots and root operations to any higher order, so he studied binomial expansion of higher order.

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