How do you find the independent of x in the expansion?
Complete step by step solution: Let (r+1) be the term independent of x. Here, we are looking for a term which is independent of x, so the power of x must be 0. Now when we know that ${(r + 1)^{th}}$ term is independent and we have also calculated the value of r, then the term independent of x will be (r+1) = 2+1= 3.
How do you find the coefficient of x 2 in binomial expansion?
Remember that Pascal’s Triangle begins with 1 as the first row and as the first and last entry of every other row. The middle terms of each row are obtained by adding the two terms from the row above. So, the coefficient of the x2 -term is 80 .
Why there is no term independent of x in the binomial expansion?
Compare the x terms and equate it to x to the power of zero which is the term independent of x. Since the value of r is a fraction, there is no term in the expansion the has the coefficient of x0 (independent of x). Note: In any binomial expansion, the r value starts from 0 followed by 1,2,3… .
How do you find the general term of a binomial expansion?
General Term: This term symbolizes all of the terms in the binomial expansion of (x + y)n. The general term in the binomial expansion of (x + y)n is Tr+1=nCrxn−ryr T r + 1 = n C r x n − r y r . Here the r-value is one less than the number of the term of the binomial expansion.
What does no term in X mean?
‘There is no term in x ‘ means that all terms in the expansion are either constants (numbers) or powers of x greater than 1 (e.g. x2 or bigger).
How do you identify independent and dependent variables?
Independent and dependent variables
- The independent variable is the cause. Its value is independent of other variables in your study.
- The dependent variable is the effect. Its value depends on changes in the independent variable.