Answer
$$48x^5 - 30x^3 - 12x^2$$
Work Step by Step
First, we use the distributive property to multiply the monomial by each term in the polynomial:
$$(6x^2)(8x^3) - (6x^2)(5x) - (6x^2)(2)$$
Multiply the coefficients and add exponents according to the product rule for exponents, which states that if the bases of two monomials are the same, we can add the exponents and keep the variable:
$$48x^{2 + 3} - 30x^{2 + 1} - 12x^2$$
Simplify by adding the exponents:
$$48x^5 - 30x^3 - 12x^2$$
