# 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.

$3x^{2}$

The simplified expression is $3x^{2}$.

#### Steps to Solve

1. Identify the expression to simplify

The expression given is $3x \cdot x$.

1. 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:

$$3x \cdot x = 3 \cdot x^{1} \cdot x^{1}$$

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 $3x^{2}$.

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.
• A common mistake is to forget that when multiplying $x \cdot x$, you must add the exponents rather than just writing $xx$.