Break Down the Algebraic Expression: Simplifying 8y into Basic Terms

Algebraic Expressions with Multiplication Notation

Break down the expression into basic terms:

8y 8y

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

8y 8y

2

Step-by-step solution

To break down the expression 8y 8y , we can see it as the multiplication of 8 8 and y y :

8y=8y 8y = 8 \cdot y

This shows the expression as a product of two factors, 8 8 and y y .

3

Final Answer

8y 8\cdot y

Key Points to Remember

Essential concepts to master this topic
  • Basic Rule: Any coefficient-variable pair represents multiplication
  • Technique: Rewrite 8y 8y as 8y 8 \cdot y using multiplication symbol
  • Check: Verify factors multiply back: 8y=8y 8 \cdot y = 8y

Common Mistakes

Avoid these frequent errors
  • Confusing breaking down with factoring
    Don't try to factor 8 into smaller numbers like 2×4 when breaking down 8y! This creates the wrong expression 2×4×y instead of 8×y. Always identify the coefficient and variable as the two basic 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 does 'breaking down into basic terms' mean?

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It means showing the simplest factors that multiply together. For 8y 8y , the basic terms are the number 8 and the variable y.

Why do we use the multiplication dot symbol?

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The dot \cdot makes the multiplication explicit and clear. In algebra, 8y 8y and 8y 8 \cdot y mean exactly the same thing!

Could I break down the 8 further into 2×4?

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No! When breaking into basic terms, we want the coefficient (8) and the variable (y) as separate factors. Breaking 8 into 2×4 creates unnecessary complexity.

What if the expression was 12xy instead?

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Then you'd have three basic terms: 12xy=12xy 12xy = 12 \cdot x \cdot y . The coefficient 12 and each variable x and y are separate factors.

Is there a difference between 8y and y×8?

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No difference at all! Multiplication is commutative, so 8y=y8=8y 8y = y \cdot 8 = 8 \cdot y . The order doesn't matter.

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