Question

which expression is equivalent to \\((3a^2bc^3)(-2ab^4c^2)\\)?

a. \\(a^2b^4c^5\\)
b. \\(-6a^2b^4c^6\\)
c. \\(-6a^3b^5c^5\\)
d. \\(6a^3b^5c^5\\)

Explanation:

Group coefficients and variables

Using the Algebraic Simplification knowledge point

$$ (3a^2bc^3)(-2ab^4c^2) = [3 \cdot (-2)] \cdot (a^2 \cdot a) \cdot (b \cdot b^4) \cdot (c^3 \cdot c^2) $$

Multiply the numerical coefficients

Using the Algebraic Simplification knowledge point

$$ 3 \cdot (-2) = -6 $$

Simplify the variable terms

Using the Exponent Rules knowledge point

$$
LATEXBLOCK0
$$

Combine all simplified parts

Using the Algebraic Simplification knowledge point

$$ -6 \cdot a^3 \cdot b^5 \cdot c^5 = -6a^3b^5c^5 $$

Answer:

• A. \(a^2b^4c^5\)
• B. \(-6a^2b^4c^6\)
• C. \(-6a^3b^5c^5\) (Correct answer)
• D. \(6a^3b^5c^5\)