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.

-3wx^2 (2x^3 + 7w^5 - 4)

Simplify your answer as much as possible.

Solution

The problem requires expanding the expression by distributing the monomial \(-3wx^2\) to each term inside the parentheses. First, distribute \(-3wx^2\) to \(2x^3\): \[ -3wx^2 \cdot 2x^3 = -6wx^{2+3} = -6wx^5 \] Next, distribute \(-3wx^2\) to \(7w^5\): \[ -3wx^2 \cdot 7w^5 = -21w^{1+5}x^2 = -21w^6x^2 \] Finally, distribute \(-3wx^2\) to \(-4\): \[ -3wx^2 \cdot (-4) = 12wx^2 \] Now combine all the terms: \[ -6wx^5 - 21w^6x^2 + 12wx^2 \] The simplified expression is: \[ -6wx^5 - 21w^6x^2 + 12wx^2 \]