1. State the problem: We want to factorize the expression $14x^{2} - 49x^{2}$. 2. Combine like terms: Since both terms have $x^{2}$, subtract the coefficients: $$14x^{2} - 49x^{2} = (14 - 49) x^{2} = -35x^{2}$$ 3. Factor out the common factor (if we treated the original expression terms separately, but since they combine to a single term, factoring as is gives $-35x^{2}$). 4. Conclusion: The expression simplifies to $-35x^{2}$, which cannot be factored further except by factoring out negative sign or $x^{2}$ depending on the context. Note: If your original intention was a different problem (like having different powers), please clarify.