Break Down the Algebraic Expression: 3y³ into Basic Terms

Q: Why don't I write the 3 as 3¹?

While technically 3 = 3¹, we don't usually write the exponent 1 because it's understood. The goal is to break down into basic terms, so 3 stays as just 3.

Q: What does 'basic terms' actually mean?

Basic terms means showing every single factor separately using multiplication. Instead of shortcuts like exponents, we write out $ y \cdot y \cdot y $ to see exactly what we're multiplying.

Q: Is there a difference between 3y³ and y³ × 3?

No difference at all! Due to the commutative property of multiplication, $ 3y^3 = y^3 \cdot 3 $. Both equal $ 3 \cdot y \cdot y \cdot y $ when broken down.

Q: How do I know when I've broken it down enough?

You're done when every factor appears separately with multiplication symbols between them. No exponents should remain - everything should be written as repeated multiplication.

Q: What if the exponent was bigger, like y⁵?

Same process! $ y^5 = y \cdot y \cdot y \cdot y \cdot y $. Just write the variable as many times as the exponent indicates, connected by multiplication symbols.

Algebraic Expressions with Exponential Decomposition

Break down the expression into basic terms:

$3y^3$

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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:

$3y^3$

Step-by-step solution

To break down the expression $3y^3$ into its basic terms, we understand the components of the expression:

$3 \, \text{is a constant multiplier}$

$y^3$ can be rewritten as $y \cdot y \cdot y$

Thus, $3y^3$ can be decomposed into $3 \cdot y \cdot y \cdot y$ .

Final Answer

$3\cdot y\cdot y \cdot y$

Key Points to Remember

Essential concepts to master this topic

Definition: Breaking down means writing each factor separately and explicitly
Technique: Rewrite $y^3$ as $y \cdot y \cdot y$ to show repeated multiplication
Check: Count factors: 3 has one factor, y appears three times ✓

Common Mistakes

Avoid these frequent errors

Applying exponent to coefficient
Don't write $3^3 \cdot y^3$ = 27y³! The exponent 3 only applies to the variable y, not the coefficient 3. Always keep the coefficient separate and only expand the exponential part.

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

Why don't I write the 3 as 3¹?

While technically 3 = 3¹, we don't usually write the exponent 1 because it's understood. The goal is to break down into basic terms, so 3 stays as just 3.

What does 'basic terms' actually mean?

Basic terms means showing every single factor separately using multiplication. Instead of shortcuts like exponents, we write out $y \cdot y \cdot y$ to see exactly what we're multiplying.

Is there a difference between 3y³ and y³ × 3?

No difference at all! Due to the commutative property of multiplication, $3y^3 = y^3 \cdot 3$ . Both equal $3 \cdot y \cdot y \cdot y$ when broken down.

How do I know when I've broken it down enough?

You're done when every factor appears separately with multiplication symbols between them. No exponents should remain - everything should be written as repeated multiplication.

What if the exponent was bigger, like y⁵?

Same process! $y^5 = y \cdot y \cdot y \cdot y \cdot y$ . Just write the variable as many times as the exponent indicates, connected by multiplication symbols.

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Break Down the Algebraic Expression: 3y³ into Basic Terms

Algebraic Expressions with Exponential Decomposition

❤️ Continue Your Math Journey!

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why don't I write the 3 as 3¹?

What does 'basic terms' actually mean?

Is there a difference between 3y³ and y³ × 3?

How do I know when I've broken it down enough?

What if the exponent was bigger, like y⁵?

🌟 Unlock Your Math Potential

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