Break Down the Algebraic Expression: Simplifying 3a Cubed

Algebraic Expressions with Exponential Terms

Break down the expression into basic terms:

3a3 3a^3

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

3a3 3a^3

2

Step-by-step solution

To break down the expression 3a3 3a^3 , we recognize that a3 a^3 means a×a×a a \times a \times a . Therefore, 3a3 3a^3 can be decomposed as 3aaa 3 \cdot a\cdot a\cdot a .

3

Final Answer

3aaa 3 \cdot a\cdot a\cdot a

Key Points to Remember

Essential concepts to master this topic
  • Exponent Rule: a3 a^3 means multiply the base three times
  • Technique: Separate coefficient from variable: 3a3=3aaa 3a^3 = 3 \cdot a \cdot a \cdot a
  • Check: Count factors: coefficient (1) plus variable factors (3) equals 4 total ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to include the coefficient when breaking down
    Don't write aaa a \cdot a \cdot a and forget the 3 = incomplete breakdown! This misses a crucial part of the expression. Always include the coefficient 3 as a separate factor: 3aaa 3 \cdot a \cdot a \cdot a .

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 can't I just write 3a3 3 \cdot a^3 ?

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While 3a3 3 \cdot a^3 is mathematically correct, the question asks to break down into basic terms. This means expanding the exponent completely to show all individual factors.

What's the difference between breaking down and factoring?

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Breaking down means writing each factor separately (like 3aaa 3 \cdot a \cdot a \cdot a ). Factoring usually means finding common factors to simplify, which is the opposite direction!

Do I always separate the coefficient from the variable?

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Yes! When breaking down algebraic expressions, treat the coefficient (number) and variable parts as separate factors. This makes it easier to see the structure of the expression.

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

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You're done when every factor is either a single number or a single variable (no exponents). Each piece should be as simple as possible!

What if the exponent was bigger, like a5 a^5 ?

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Same process! a5=aaaaa a^5 = a \cdot a \cdot a \cdot a \cdot a (five copies of a). Always write the base as many times as the exponent indicates.

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