Question

/Below is the Pascal's Triangle. It is related to the coefficients of the expansion of the binomial (a + b) (a + b) (a + b) (a + b) 3 (a + b) 6 (a+b) 5 10 10 5 1 1 1 1 3 1 1 a) What is the pattern in the triangle? b) Use this pattern to find the coefficients of(a+b). i.e. what is the next line?

Please help me with this problem. I have no clue where to even start

Answer 1

Catby² = cathy catb) (arb) =[ a² + ab + ab +6²] Carb) = [a²+ 2ab + b2] (a+b) = a3+2a²b+ ab + a²b + 2ab²th =a3+3a2b+sab²+b3 Here coefficients are. 1 which is 4th line in pascal's triangle. Yes, we can use this pattern for expansion of Ca-byn. By taking (a-b)"= [atc-by]". Mow, Ca-bi?= [anib)]3 =a²+ 3 a² (-6) +39(-6)² = a3_ 3a²b + 3 a6²-b3 fche

- The pattern is as follows 1 add. add add. add and & add.x ی . consider pattern. 1 2 1 6 3 To 10 - 6 15 6 Hence, coefficients of carb) o are. 6 15 2o Pe. Carb)&= a + bas b + 15046² + 15 a ²64 +6 abstbe. +2003 63