How do you do this problem 3x times x squared
The Correct answer and Explanation is:
To solve the expression 3x×x23x \times x^23x×x2, we start by recognizing that we are dealing with a multiplication of terms involving the same base, which is xxx.
Step-by-Step Solution
- Identify the Terms: The expression consists of two terms: 3x3x3x and x2x^2×2. Here, 333 is a coefficient (a number that multiplies a variable), xxx is the variable, and x2x^2×2 indicates xxx is raised to the second power.
- Apply the Law of Exponents: When multiplying terms with the same base, you can add their exponents. The exponent for xxx in 3x3x3x is 111 (since xxx can be written as x1x^1×1). Therefore, we can rewrite the multiplication as follows:3×1×x23x^1 \times x^23×1×x2
- Combine the Exponents: According to the exponent multiplication rule xa×xb=xa+bx^a \times x^b = x^{a+b}xa×xb=xa+b:x1×x2=x1+2=x3x^1 \times x^2 = x^{1+2} = x^3×1×x2=x1+2=x3
- Multiply the Coefficients: Next, we multiply the coefficients:3×1=33 \times 1 = 33×1=3
- Final Expression: Combining both the coefficient and the variable, we obtain:3x33x^33×3
Final Answer
Thus, the final answer to the problem 3x×x23x \times x^23x×x2 is:3×3\boxed{3x^3}3×3
Explanation
The key principles used in solving this expression involve basic algebraic operations and the laws of exponents. When multiplying two terms with the same base, you simply add the exponents. This property of exponents is fundamental in algebra and is essential for simplifying expressions.
In this case, we first identified the components of the expression, focusing on the coefficients and the variables. After applying the multiplication rule for exponents, we combined the terms and simplified the expression. This method allows us to handle more complex algebraic expressions efficiently, maintaining clarity and accuracy throughout the process. Mastery of these principles is crucial for advancing in mathematics, as they form the basis for solving equations and manipulating polynomials in various mathematical contexts.