Simplify: What Is 3x Times x?
The question “what is 3x times x” asks to multiply two algebraic factors: \(3x\) and \(x\). In math algebra, this is a multiplication of monomials (single-term expressions). The key ideas are: multiply the numerical coefficients and then combine like variable factors using exponent rules.
Rule: When multiplying powers with the same base, add exponents: \(\;x^a \cdot x^b = x^{a+b}\).
Step 1: Rewrite each factor clearly
The expression \(3x\) means \(3 \cdot x\). Also, \(x\) can be written as \(x^1\) to show its exponent.
\[ 3x \cdot x = (3 \cdot x) \cdot x^1 \]
Step 2: Multiply the coefficient
The coefficient is the numerical part. Here, the only coefficient is 3, so it stays 3 after multiplication:
\[ (3 \cdot x) \cdot x^1 = 3 \cdot (x \cdot x^1) \]
Step 3: Combine the x factors using exponents
Since \(x = x^1\), the variable part becomes:
\[ x \cdot x^1 = x^1 \cdot x^1 = x^{1+1} = x^2 \]
Therefore:
\[ 3 \cdot (x \cdot x) = 3x^2 \]
Final simplified form: \(\boxed{3x^2}\).
Quick check with a number (optional)
If \(x = 2\), then the original product is \(3x \cdot x = (3 \cdot 2)\cdot 2 = 6 \cdot 2 = 12\). The simplified expression gives \(3x^2 = 3 \cdot 2^2 = 3 \cdot 4 = 12\). The results match.
Summary table
| Expression | Action | Result |
|---|---|---|
| \(3x \cdot x\) | Rewrite \(x\) as \(x^1\) | \(3x \cdot x^1\) |
| \(x^1 \cdot x^1\) | Add exponents | \(x^{1+1} = x^2\) |
| \(3 \cdot x^2\) | Combine coefficient and variable | \(3x^2\) |
Visualization: Combining factors into a power
Final answer
\[ 3x \cdot x = 3x^2 \]