Break Down the Algebraic Expression: Analyzing 5x²

The exponent only affects the variable directly next to it. In $5x^2$, the 2 only applies to x, so you get $5 \cdot x \cdot x$, not $25x$.

Look for multiplication signs (even invisible ones!). In $5x^2$, there's an invisible multiplication between 5 and $x^2$, giving us three separate factors: 5, x, and x.

$5x^2 = 5 \cdot x \cdot x$, but $(5x)^2 = 5x \cdot 5x = 25x^2$. The parentheses make a huge difference - they group the 5 and x together before applying the exponent!

Yes! $5 \cdot x \cdot x$ can also be written as $x \cdot 5 \cdot x$ or $x \cdot x \cdot 5$. Multiplication is commutative, so the order doesn't matter.

Breaking expressions into basic factors helps you understand the structure and makes advanced topics like factoring polynomials much easier. It's like taking apart a machine to see how it works!