Break Down the Expression: Rewriting 6z² + z Into Basic Components

Q: What does 'basic components' mean exactly?

Basic components means showing every single multiplication factor separately. For $ 6z^2 $, you write it as 6 · z · z to show the coefficient 6 and both z factors clearly.

Q: Why do I need to write 1·z instead of just z?

Writing $ 1 \cdot z $ shows the implied coefficient of 1. This helps you see that every term has a coefficient, even when it's not written explicitly.

Q: Is this the same as factoring?

No! Factoring would give you $ z(6z + 1) $. Breaking into basic components shows all individual factors: $ 6 \cdot z \cdot z + 1 \cdot z $.

Q: How is this different from just rearranging terms?

Rearranging changes the order of terms, like writing $ z + 6z^2 $. Basic components break down the structure within each term to show all multiplication factors.

Q: What if there are more variables like xy²?

Apply the same principle! $ 3xy^2 $ becomes $ 3 \cdot x \cdot y \cdot y $. Show the coefficient and every variable factor separately.

Algebraic Expressions with Coefficient Decomposition

Rewrite using basic components:

$6z^2 + z$

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Step-by-step written solution

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Understand the problem

Rewrite using basic components:

$6z^2 + z$

Step-by-step solution

To rewrite the expression $6z^2 + z$ , break it down into basic components:

The term $6z^2$ can be expressed as $6 \cdot z \cdot z$ .

The term $z$ is $1 \cdot z$ .

Thus, rewriting gives $6 \cdot z \cdot z + 1 \cdot z$ .

Final Answer

$6\cdot z\cdot z + 1\cdot z$

Key Points to Remember

Essential concepts to master this topic

Basic Components: Break coefficients and variables into individual multiplication factors
Technique: Rewrite 6z² as 6·z·z and z as 1·z
Check: Verify each term shows all multiplication factors explicitly ✓

Common Mistakes

Avoid these frequent errors

Confusing basic components with factoring
Don't rewrite 6z² + z as z(6z + 1) = factored form! This is factoring, not breaking into basic components. Always show each coefficient and variable as separate multiplication factors like 6·z·z + 1·z.

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 'basic components' mean exactly?

Basic components means showing every single multiplication factor separately. For $6z^2$ , you write it as 6 · z · z to show the coefficient 6 and both z factors clearly.

Why do I need to write 1·z instead of just z?

Writing $1 \cdot z$ shows the implied coefficient of 1. This helps you see that every term has a coefficient, even when it's not written explicitly.

Is this the same as factoring?

No! Factoring would give you $z(6z + 1)$ . Breaking into basic components shows all individual factors: $6 \cdot z \cdot z + 1 \cdot z$ .

How is this different from just rearranging terms?

Rearranging changes the order of terms, like writing $z + 6z^2$ . Basic components break down the structure within each term to show all multiplication factors.

What if there are more variables like xy²?

Apply the same principle! $3xy^2$ becomes $3 \cdot x \cdot y \cdot y$ . Show the coefficient and every variable factor separately.

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