Break Down the Expression: Identifying Terms in 3x² + 2x

Algebraic Expressions with Multiplication Terms

Break down the expression into basic terms:

3x2+2x 3x^2 + 2x

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

3x2+2x 3x^2 + 2x

2

Step-by-step solution

The expression can be broken down as follows:

3x2+2x 3x^2 + 2x

Breaking down each term we have:

- 3x2 3x^2 becomes 3xx 3\cdot x\cdot x

- 2x 2x remains 2x 2 \cdot x

Finally, the expression is:

3xx+2x 3\cdot x\cdot x+2\cdot x

3

Final Answer

3xx+2x 3\cdot x\cdot x+2\cdot x

Key Points to Remember

Essential concepts to master this topic
  • Terms: Each part separated by addition or subtraction signs
  • Technique: Break 3x2 3x^2 into 3xx 3\cdot x\cdot x
  • Check: Count multiplication symbols in each term: first has 3 parts, second has 2 ✓

Common Mistakes

Avoid these frequent errors
  • Adding extra terms when breaking down expressions
    Don't split 3x2 3x^2 into 3x2+x 3\cdot x^2 + x = wrong number of terms! This creates extra terms that weren't in the original expression. Always keep the same number of terms when breaking down multiplication.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

\( 4x^2 + 6x \)

FAQ

Everything you need to know about this question

What's the difference between a term and a factor?

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A term is a complete part of an expression separated by + or - signs. A factor is what gets multiplied together within each term. In 3x2 3x^2 , the whole thing is one term with factors 3, x, and x.

Why don't we break down the coefficient 3?

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Numbers like 3 are already in their simplest form as factors. We only break down variables with exponents like x2 x^2 into repeated multiplication: xx x \cdot x .

How do I know when to stop breaking down terms?

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Stop when you have only numbers and single variables being multiplied together. If you see any exponents on variables, keep breaking them down into repeated multiplication.

What if the expression was 3x² - 2x instead?

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The breakdown works the same way! You'd get 3xx2x 3\cdot x\cdot x - 2\cdot x . The subtraction sign stays between the terms.

Is 2x the same as 2·x?

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Yes! When a number is written next to a variable like 2x 2x , it means multiplication. Writing 2x 2\cdot x just makes the multiplication explicit.

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