What is the simplified form of (3x²)(4x³)?

What is the simplified form of (3x²)(4x³)?

• A. 7x⁵
• B. 10x⁵
• C. 12x⁵
• D. 15x⁵

Answer: (C)

To simplify the expression (3x²)(4x³), you start by applying the associative and commutative properties of multiplication. First, multiply the coefficients (the numerical parts) together: 3 * 4 = 12. Next, for the variables with exponents, you add the exponents when you multiply like bases: x² * x³ = x^(2+3) = x⁵. Combining both parts, the simplified expression becomes: 12x⁵. Thus, the correct answer is 12x⁵, which matches the answer choice provided. This process of multiplying coefficients and adding exponents is a foundational principle in algebra that helps in simplifying polynomial expressions.

To simplify the expression (3x²)(4x³), you start by applying the associative and commutative properties of multiplication.

First, multiply the coefficients (the numerical parts) together:

3 * 4 = 12.

Next, for the variables with exponents, you add the exponents when you multiply like bases:

x² * x³ = x^(2+3) = x⁵.

Combining both parts, the simplified expression becomes:

12x⁵.

Thus, the correct answer is 12x⁵, which matches the answer choice provided. This process of multiplying coefficients and adding exponents is a foundational principle in algebra that helps in simplifying polynomial expressions.