The binomial theorem and Pascal's triangle
See (a + b)³ as three brackets and count the paths that give each term, read the coefficients from Pascal's triangle, and use them for expansions with numbers.
- سوريا: الصف ١١
- فلسطين: الصف ١٠
- أفغانستان: الصف ١١
- روسيا: الصف ١٠
- فرنسا: الصف ١٢
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
This studio follows Afghan grade 11 chapter 9 (the binomial theorem and Pascal's triangle) and the UK A-level binomial expansion.
In (a + b)٣ each of the three brackets gives an a or a b. A path in the tree is one such choice. The coefficient of a٢b is the number of paths with two a's and one b: the number of ways to choose which bracket gives the b.
Common mistakes worked on here: counting letters instead of paths, forgetting the numbers inside the brackets, taking a neighbouring term of Pascal's row, and thinking the coefficients add up to n.