1. **State the problem:** Simplify and analyze the expression $3^x \times (3^x - 11)$. 2. **Recall the formula:** When multiplying terms with the same base, use the property $a^m \times a^n = a^{m+n}$. Here, we have a product of $3^x$ and $(3^x - 11)$, which is a binomial expression. 3. **Expand the expression:** Use distributive property: $$3^x \times (3^x - 11) = 3^x \times 3^x - 3^x \times 11$$ 4. **Simplify powers:** $$3^x \times 3^x = 3^{x+x} = 3^{2x}$$ 5. **Rewrite the expression:** $$3^{2x} - 11 \times 3^x$$ 6. **Factor the expression:** Notice $3^x$ is common: $$3^x(3^x - 11)$$ (which is the original expression, so this confirms the factorization). 7. **Summary:** The expression simplifies to $$3^{2x} - 11 \times 3^x$$ which can be factored back to $$3^x(3^x - 11)$$. This is a quadratic form in terms of $3^x$. **Final answer:** $$3^{2x} - 11 \times 3^x$$