P(x)=(xn​)pxqn−x

To answer the question, we need to understand the given expression P(x) = (xn)pxqn-x.

Step 1: Simplify the expression inside the parentheses. The expression (xn) means raising x to the power of n. So, we can rewrite it as xn.

Step 2: Rewrite the expression using the power rule. The power rule states that (xa)b = xab. Applying this rule, we can rewrite the expression as xn * px * qn-x.

Step 3: Simplify the expression further. Multiplying xn and px gives us x(n+1). Multiplying qn-x is equivalent to dividing qn by qx. So, we can rewrite the expression as x(n+1) * px * (qn/qx).

Step 4: Simplify the expression using the division rule. The division rule states that (a/b)c = ac/bc. Applying this rule, we can rewrite the expression as x(n+1) * px * qn/qx.

Step 5: Simplify the expression by canceling out common factors. We can cancel out the common factor of x in the numerator and denominator, resulting in x * px * qn-1/q.

Step 6: Simplify the expression further. Multiplying x and px gives us x(px+1). So, the final simplified expression is x(px+1) * qn-1/q.

Therefore, the simplified form