Binomial Theorem
Properties of Binomial Expansion
IIT-JEE 2009
Grade 11
Question:
The number of distinct terms in the expansion of $(1 + x)^{101}(1 + x^2 - x)^{100}$, when expressed as a polynomial in $x$, is:
(1) $202$
(2) $201$
(3) $200$
(4) $101$
Step-by-Step Solution
Key Concept: First simplify the product $(1 + x)(1 - x + x^2)$ to a familiar binomial form, and use this to rewrite the entire expression as $(1 + x)(1 + x^3)^{100}$ before counting distinct powers of $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)