Breaking Down the Expression: Identify Terms in 3y² + 6

Algebraic Expressions with Multiplication Notation

Break down the expression into basic terms:

3y2+6 3y^2 + 6

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

3y2+6 3y^2 + 6

2

Step-by-step solution

To break down the expression 3y2+6 3y^2 + 6 , we need to recognize common factors or express terms in basic forms.

The term 3y2 3y^2 can be rewritten by breaking down the operations: 3yy 3\cdot y\cdot y .

The constant 6 6 remains as it is in its basic term.

Thus, the broken down expression becomes 3yy+6 3\cdot y\cdot y + 6 .

3

Final Answer

3yy+6 3\cdot y\cdot y+6

Key Points to Remember

Essential concepts to master this topic
  • Basic Terms: Express each part using fundamental multiplication and addition operations
  • Technique: Rewrite 3y2 3y^2 as 3yy 3 \cdot y \cdot y to show multiplication
  • Check: Verify that 3yy+6 3 \cdot y \cdot y + 6 equals original expression ✓

Common Mistakes

Avoid these frequent errors
  • Incorrectly breaking down exponents
    Don't write 3y2 3y^2 as 3yy2 3 \cdot y \cdot y \cdot 2 = wrong interpretation! The exponent 2 means y is multiplied by itself, not that 2 is a separate factor. Always remember that y2=yy y^2 = y \cdot y , not y2 y \cdot 2 .

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 does it mean to break down an expression into basic terms?

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Breaking down means showing all the multiplication and addition operations explicitly. Instead of using shortcuts like exponents, we write out what each part actually represents.

Why do we write y² as y·y instead of keeping it as y²?

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Writing y2 y^2 as yy y \cdot y shows the basic multiplication operation. This helps you understand that an exponent means repeated multiplication of the base.

Should I break down the coefficient 3 further?

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No, the coefficient 3 is already in its simplest form. We only break down parts that have hidden operations like exponents or can be factored differently.

What about the constant 6? Can I break it down?

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The constant 6 stays as 6 unless the problem specifically asks you to factor it (like 2×3 2 \times 3 ). In this context, 6 is already a basic term.

How is this different from factoring?

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Breaking down shows individual operations within each term, while factoring finds common factors between terms. Here we're expanding 3y2 3y^2 to show its structure, not looking for shared factors.

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