To simplify the given expression, we can distribute the 6ab term to both terms inside the parentheses:
6ab(4b^2c + 3a^2) = (6ab)(4b^2c) + (6ab)(3a^2)
Simplifying further, we can multiply the coefficients and add the exponents with like bases:
(6ab)(4b^2c) = (6 * 4)(a * b)(b^2 * c) = 24ab^3c
Similarly,
(6ab)(3a^2) = (6 * 3)(a * a)(b * b) = 18a^2b^2
Therefore, the simplified expression is:
24ab^3c + 18a^2b^2
6ab(4b^2c + 3a^2).
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