Binomial Expansion

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

 

Binomial Theorem

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 and Factoring

Special Products
1.   $(x + y)(x - y) = x^2 - y^2$

2.   $(x + y)^2 = x^2 + 2xy + y^2$

3.   $(x - y)^2 = x^2 - 2xy + y^2$

 
 
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