Final answer:
The mathematical process applied in the expression 3x²(2x - 6x² + 7) is the Distributive Property. Multiplying the monomial with each term in the parentheses results in expanded form 6x³ - 18x´ + 21x², illustrating the application of this property.
Step-by-step explanation:
The question pertains to determining which mathematical process is being applied in the given expression. Specifically, it refers to the process of multiplication of a monomial and a polynomial. The correct option that describes this process is D. Distributive Property:
- Applying the distributive property to the expression 3x²(2x - 6x² + 7) would involve multiplying 3x² with each term inside the parentheses.
- The result of this multiplication would be 6x³ - 18x´ + 21x², which represents the expanded form of the given expression.
- To execute this, each term inside the parentheses is multiplied by the monomial 3x².
- This process differs from the other options like Adding Polynomials, Combining Like Terms, Difference of Two Squares (DOTS), and the other examples provided.
In summary, the rule described by xPx9 = x(p+q) aligns with the properties of exponents when multiplying expressions with the same base.