In the expansion of (1 + x)^p (1 + x)^q, if the coefficient of x³ is 35, then what is the value of (p + q)? 

7Concept:

Binomial Expansion:

• The binomial theorem is used to expand expressions of the form \((1 + x)^n\).
• The general term in the expansion of \((1 + x)^n\) is given by \(T_k = C(n, k) \cdot x^k\), where ⁿC_k is the binomial coefficient.
• To find the coefficient of x^3, we identify the corresponding terms from the expansion and set the coefficient equal to 35.

Calculation:

Given the expansion of \((1 + x)^p \cdot (1 + x)^q\), we have:

The coefficient of x³ in  the expansion is 35.

We use the binomial expansion formula for the term x³

⇒ (p+ q)_c3 = 35 = ⁷C₃

⇒ p+q =7

∴ the correct answer is Option C