Find the term independent of x in the expansion of a given binomial
Problem
Find the term that is independent of x in the expansion of $\left( 2 + \dfrac{3}{x^2} \right)\left( x - \dfrac{2}{x} \right)^6$.
A. 180 | C. -140 |
B. 160 | D. -160 |
Problem
Find the term that is independent of x in the expansion of $\left( 2 + \dfrac{3}{x^2} \right)\left( x - \dfrac{2}{x} \right)^6$.
A. 180 | C. -140 |
B. 160 | D. -160 |
The Expansion of (a + b)n
If $n$ is any positive integer, then
$(a + b)^n = a^n + {_nC_1}a^{n - 1}b + {_nC_2}a^{n - 2}b^2 + \, \cdots \, + {_nC_m}a^{n - m}b^m + \, \cdots \, + b^n$
Where
${_nC_m}$ = combination of n objects taken m at a time.
Special Products
1. $(x + y)(x - y) = x^2 - y^2$
2. $(x + y)^2 = x^2 + 2xy + y^2$
3. $(x - y)^2 = x^2 - 2xy + y^2$