Break Down the Expression: Simplifying 4a²

Algebraic Expressions with Exponent Breakdown

Break down the expression into basic terms:

4a2 4a^2

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Step-by-step written solution

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1

Understand the problem

Break down the expression into basic terms:

4a2 4a^2

2

Step-by-step solution

To break down the expression 4a2 4a^2 into basic terms, we need to look at each factor:

4is a constant multiplier 4 \, \text{is a constant multiplier}

a2 a^2 means aa a \cdot a

Hence, 4a2 4a^2 is equivalent to 4aa 4 \cdot a \cdot a .

3

Final Answer

4aa 4\cdot a\cdot a

Key Points to Remember

Essential concepts to master this topic
  • Definition: Breaking down means writing as separate factors multiplied together
  • Technique: Expand a2 a^2 into aa a \cdot a to show multiplication
  • Check: Count factors: 4aa 4 \cdot a \cdot a has three factors total ✓

Common Mistakes

Avoid these frequent errors
  • Confusing coefficient with exponent
    Don't write 42a 4^2 \cdot a or 4a 4 \cdot a = wrong breakdown! The 4 is multiplied by a2 a^2 , not squared itself or applied only once. Always expand the exponent part: a2=aa a^2 = a \cdot a .

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

\( 2x^2 \)

FAQ

Everything you need to know about this question

What does it mean to 'break down' an expression?

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Breaking down means writing the expression as a product of its simplest factors. Instead of using shortcuts like exponents, you show every multiplication explicitly.

Why can't I just write 4a2 4 \cdot a^2 ?

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That's not fully broken down! You still have the exponent a2 a^2 . To break it down completely, expand a2 a^2 into aa a \cdot a .

What if the exponent was 3 or higher?

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Same rule applies! 4a3 4a^3 would become 4aaa 4 \cdot a \cdot a \cdot a . The exponent tells you how many times to write the variable as a factor.

Does the order of factors matter?

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No! 4aa 4 \cdot a \cdot a , a4a a \cdot 4 \cdot a , and aa4 a \cdot a \cdot 4 are all equivalent. Multiplication is commutative, meaning you can rearrange factors.

How do I remember what a2 a^2 means?

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Think of it as 'a squared' = a × a. The little 2 tells you to use 'a' as a factor exactly 2 times in your multiplication.

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