Break Down the Expression 2x²: Term by Term Analysis

Q: What does 'basic terms' actually mean?

Basic terms are the simplest building blocks of an expression - numbers and single variables without exponents. We break down $ x^2 $ into $ x \cdot x $ to show these basic pieces.

Q: Could I write it as 2xx instead of 2·x·x?

While mathematically equivalent, using multiplication dots makes it clearer that we have separate factors. This helps distinguish between $ 2 \cdot x \cdot x $ and something like $ 2xx $ which might be confusing.

Q: Is there a difference between x² and x·x?

No difference in value! $ x^2 $ is just shorthand notation for $ x \cdot x $. Breaking it down helps us see the individual factors more clearly.

Q: What if the expression was 3x³? How would I break that down?

You'd write it as $ 3 \cdot x \cdot x \cdot x $! The coefficient stays the same, and $ x^3 $ becomes three separate x factors.

Algebraic Expressions with Basic Factorization

Break down the expression into basic terms:

$2x^2$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Break down the expression into basic terms:

$2x^2$

Step-by-step solution

The expression $2x^2$ can be factored and broken down into the following basic terms:

The coefficient $2$ remains as it is since it is already a basic term.
The term $x^2$ can be broken down into $x \cdot x$ .
Therefore, the entire expression can be written as $2 \cdot x \cdot x$ .

This breakdown helps in understanding the multiplicative nature of the expression.

Among the provided choices, the correct one that matches this breakdown is choice 2: $2\cdot x\cdot x$ .

Final Answer

$2\cdot x\cdot x$

Key Points to Remember

Essential concepts to master this topic

Rule: Break down exponents into repeated multiplication factors
Technique: Convert $x^2$ to $x \cdot x$ for basic terms
Check: Verify by counting factors: $2 \cdot x \cdot x$ has 3 factors ✓

Common Mistakes

Avoid these frequent errors

Applying exponents to coefficients incorrectly
Don't write $2x^2$ as $2^2 \cdot x^2$ = wrong factorization! The exponent only applies to the variable x, not the coefficient 2. Always keep coefficients separate and only break down the variable's exponent.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 2x^2 $$

FAQ

Everything you need to know about this question

Why don't we change the coefficient 2 when breaking down the expression?

The coefficient 2 is already in its simplest form as a basic term. Only the variable part $x^2$ needs to be broken down because it contains an exponent.

What does 'basic terms' actually mean?

Basic terms are the simplest building blocks of an expression - numbers and single variables without exponents. We break down $x^2$ into $x \cdot x$ to show these basic pieces.

Could I write it as 2xx instead of 2·x·x?

While mathematically equivalent, using multiplication dots makes it clearer that we have separate factors. This helps distinguish between $2 \cdot x \cdot x$ and something like $2xx$ which might be confusing.

Is there a difference between x² and x·x?

No difference in value! $x^2$ is just shorthand notation for $x \cdot x$ . Breaking it down helps us see the individual factors more clearly.

What if the expression was 3x³? How would I break that down?

You'd write it as $3 \cdot x \cdot x \cdot x$ ! The coefficient stays the same, and $x^3$ becomes three separate x factors.

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