What is 3x times 2x squared????
The Correct Answer and Explanation is:
To solve the expression (3x \times 2x^2), we need to multiply the coefficients (numerical parts) and the variable parts separately.
Step-by-Step Solution:
- Identify Coefficients and Variables:
- The coefficients are (3) and (2).
- The variable part consists of (x) and (x^2).
- Multiply the Coefficients:
- (3 \times 2 = 6)
- Multiply the Variables:
- When multiplying variables, we add their exponents. The exponent of (x) is (1) (since (x) can be written as (x^1)), and the exponent of (x^2) is (2).
- Therefore, we have:
[
x^1 \times x^2 = x^{1+2} = x^3
]
- Combine Results:
- Now, combine the results from the coefficient multiplication and the variable multiplication:
[
6 \times x^3 = 6x^3
]
Final Answer:
The product of (3x) and (2x^2) is (6x^3).
Explanation:
When multiplying algebraic expressions, we follow the distributive property and the rules of exponents. The distributive property states that for any numbers (a), (b), and (c):
[
a(b + c) = ab + ac
]
This property extends to algebraic terms, allowing us to simplify expressions efficiently.
In this problem, we first focus on multiplying the numerical coefficients. This straightforward step involves basic arithmetic, resulting in (6).
The more complex part of the multiplication involves the variable (x). The rules of exponents state that when you multiply like bases, you add the exponents. This is crucial for simplifying expressions involving variables.
Thus, understanding these foundational algebraic principles enables us to solve expressions involving multiplication accurately. The final expression (6x^3) tells us that we have a polynomial of degree (3), which indicates the highest power of the variable present. This form is essential in algebra, especially when we analyze functions or equations involving multiple terms and variables.
In summary, (3x \times 2x^2 = 6x^3) showcases both arithmetic and algebraic rules working in harmony.