Breaking Down the Expression: 4x² + 6x into Basic Terms

Expression Decomposition with Polynomial Terms

Break down the expression into basic terms:

4x2+6x 4x^2 + 6x

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

4x2+6x 4x^2 + 6x

2

Step-by-step solution

To break down the expression4x2+6x 4x^2 + 6x into its basic terms, we need to look for a common factor in both terms.

The first term is 4x2 4x^2 , which can be rewritten as 4xx 4\cdot x\cdot x .

The second term is6x 6x , which can be rewritten as 23x 2\cdot 3\cdot x .

The common factor between the terms is x x .

Thus, the expression can be broken down into 4x2+6x 4\cdot x^2 + 6\cdot x , and further rewritten with common factors as 4xx+6x 4\cdot x\cdot x + 6\cdot x .

3

Final Answer

4xx+6x 4\cdot x\cdot x+6\cdot x

Key Points to Remember

Essential concepts to master this topic
  • Basic Terms: Break each coefficient and variable into separate multiplication factors
  • Technique: Rewrite 4x2 4x^2 as 4xx 4 \cdot x \cdot x and 6x 6x as 6x 6 \cdot x
  • Check: Verify by multiplying back: 4xx+6x=4x2+6x 4 \cdot x \cdot x + 6 \cdot x = 4x^2 + 6x

Common Mistakes

Avoid these frequent errors
  • Confusing factoring with decomposing into basic terms
    Don't factor out common terms like 2x(2x + 3) = wrong approach! This creates factored form, not basic multiplication terms. Always break down each term into its individual coefficient and variable factors.

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 basic terms and factoring?

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Basic terms show each coefficient and variable as separate factors: 4xx+6x 4 \cdot x \cdot x + 6 \cdot x . Factoring groups common factors: 2x(2x+3) 2x(2x + 3) . They're different processes!

Why write x² as x·x instead of just x²?

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Breaking x2 x^2 into xx x \cdot x shows the basic multiplication structure. This helps you see exactly what's being multiplied together, which is essential for understanding polynomial operations.

Do I need to break down the numbers too?

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For basic term decomposition, you typically keep whole number coefficients like 4 and 6 as single factors. Only break them down if specifically asked for prime factorization.

How is this different from distributing?

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This is the opposite of distributing! Here you're expanding each term to show all its factors. Distributing would combine terms, while decomposing separates them into basic parts.

What if there are more terms in the expression?

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Apply the same process to each term individually. Break down every coefficient and variable into its basic factors, keeping the addition signs between terms.

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