Simplify “5 x 2 x”
The keyword 5 x 2 x is naturally interpreted in math algebra as a product of factors: \(5\cdot x\cdot 2\cdot x\). The goal is to simplify the expression by multiplying numerical coefficients and combining repeated variable factors using exponent rules.
Simplified form: \(5\cdot x\cdot 2\cdot x=10x^2\).
1) Group Numerical Factors and Variable Factors
Reorder the factors (multiplication is commutative) so like parts are together: \(5\cdot x\cdot 2\cdot x=(5\cdot 2)\cdot (x\cdot x)\).
2) Multiply the Coefficients
The numerical coefficient is \(5\cdot 2=10\).
3) Combine Like Variable Factors Using Exponents
The variable part is \(x\cdot x=x^2\), because multiplying the same base adds exponents: \(x^1\cdot x^1=x^{1+1}=x^2\).
\[ 5\cdot x\cdot 2\cdot x =(5\cdot 2)\cdot(x\cdot x) =10\cdot x^2 =10x^2 \]
4) Summary Table of the Simplification
| Part | Expression | Simplifies to |
|---|---|---|
| Numbers (coefficients) | \(5\cdot 2\) | \(10\) |
| Variables | \(x\cdot x\) | \(x^2\) |
| Combined | \((5\cdot 2)\cdot(x\cdot x)\) | \(10x^2\) |
5) Visualization: Factor Grouping to \(10x^2\)
Interpreting “5 x 2 x” as \(5\cdot x\cdot 2\cdot x\) yields the simplified algebraic expression \(10x^2\).