Question: Rewrite without parentheses. -7bc^4(3b^5 - 2b^3c^6 + 4c^6) Simplify your answer as much as…

Rewrite without parentheses. -7bc^4(3b^5 - 2b^3c^6 + 4c^6) Simplify your answer as much as possible.

Solution

To simplify the expression by removing the parentheses and distributing, follow these steps: Given expression: \[ -7b^4c\left(3b^5 - 2b^3c^6 + 4c^6\right) \] Distribute \(-7b^4c\) to each term inside the parentheses: First term: \[ -7b^4c \cdot 3b^5 = -21b^{9}c \] Second term: \[ -7b^4c \cdot (-2b^3c^6) = 14b^{7}c^{7} \] Third term: \[ -7b^4c \cdot 4c^6 = -28b^4c^{7} \] Combine all terms to get the simplified expression: \[ -21b^9c + 14b^7c^7 - 28b^4c^7 \]