What is 3x multiplied by x?
Understand the Problem
The question is asking us to simplify the expression 3x multiplied by x, which requires applying the rules of algebra for multiplication of variables.
Answer
$3x^{2}$
Answer for screen readers
The simplified expression is $3x^{2}$.
Steps to Solve
- Identify the expression to simplify
The expression given is $3x \cdot x$.
- Apply the multiplication rule for variables
When multiplying variables, you combine the coefficients and add the exponents of the same base. The coefficient is 3, and the variable is $x$.
- The multiplication can be simplified as follows:
$$ 3x \cdot x = 3 \cdot x^{1} \cdot x^{1} $$
- Combine the terms
Since the bases are the same ($x$), we can add the exponents:
$$ x^{1} \cdot x^{1} = x^{1+1} = x^{2} $$
So the expression now becomes:
$$ 3 \cdot x^{2} = 3x^{2} $$
The simplified expression is $3x^{2}$.
More Information
This expression $3x^{2}$ represents a quadratic expression where 3 is the coefficient of $x^2$. Quadratics are fundamental in algebra and are often found in various applications, such as physics and economics.
Tips
- A common mistake is to forget that when multiplying $x \cdot x$, you must add the exponents rather than just writing $xx$.
- Another mistake is neglecting to multiply the coefficients or incorrectly simplifying the expression.