1. Stating the problem: We need to verify if the expression $(q^2-2)x^2(-9x^6y^7+11)$ can be rewritten as $x^2[(q^2-2)x^2(-9x^6y^7+11)]$. 2. Start with the original expression: $$ (q^2-2)x^2(-9x^6y^7+11) $$ 3. Look at the proposed rewritten expression: $$ x^2[(q^2-2)x^2(-9x^6y^7+11)] $$ 4. Simplify inside the brackets in the rewritten expression: Inside the brackets is $$ (q^2-2)x^2(-9x^6y^7+11) $$ which is exactly the original expression. 5. Multiply the outside $x^2$ by the inside expression: $$ x^2 \times (q^2-2)x^2(-9x^6y^7+11) = (q^2-2)x^4(-9x^6y^7+11) $$ 6. Comparing the two expressions: Original: $$ (q^2-2)x^2(-9x^6y^7+11) $$ Rewrite: $$ (q^2-2)x^4(-9x^6y^7+11) $$ They are not equal unless $x^2=1$ or $x=\pm 1$. Final answer: No, the original expression cannot be written as stated because the rewritten expression has an extra factor of $x^2$ which changes its value.