Question: Algebra and Geometry Review Multiplying a multivariate polynomial by a monomial Rewrite without…

Algebra and Geometry Review Multiplying a multivariate polynomial by a monomial

Rewrite without parentheses.

-2wx^2(6w^4 + 8w^5x^6 - 9x^6)

Simplify your answer as much as possible.

Solution

To solve the problem, we need to distribute \( -2w^2 \) to each term inside the parentheses: \[ -2w^2 \left(6w^4 + 8w^5x^6 - 9x^6\right) \] Distribute \( -2w^2 \) to each term: First term: \[ -2w^2 \times 6w^4 = -12w^{6} \] Second term: \[ -2w^2 \times 8w^5x^6 = -16w^7x^6 \] Third term: \[ -2w^2 \times (-9x^6) = 18w^2x^6 \] Combine all the terms: \[ -12w^{6} - 16w^7x^6 + 18w^2x^6 \] This is the expression simplified as much as possible.