Rewrite 8x² - 4x Using Basic Components: Step-by-Step Guide

Q: What's the difference between basic components and factoring?

Basic components means breaking each term into its individual parts. Factoring means pulling out common factors. For $ 8x^2 - 4x $, basic components = $ 8 \cdot x \cdot x - 4 \cdot x $, but factored form = $ 4x(2x - 1) $.

Q: Why write x twice in the first term?

Because $ x^2 $ means x times x! When showing basic components, we write out each factor separately: $ x^2 = x \cdot x $.

Q: Do I need to show multiplication signs?

Yes! Basic components require showing all multiplication explicitly. Use $ \cdot $ symbols between each factor to make it clear: $ 8 \cdot x \cdot x $, not $ 8xx $.

Q: How is this different from expanding?

Expanding means multiplying out brackets like $ (x+2)(x+3) $. Basic components means breaking down existing terms into their individual factors without any brackets.

Factoring Expressions with Basic Component Breakdown

Rewrite using basic components:

$8x^2 - 4x$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Rewrite using basic components:

$8x^2 - 4x$

Step-by-step solution

To rewrite the expression $8x^2 - 4x$ using its basic components, we'll follow these steps:

Step 1: Identify the greatest common factor of the terms.
Step 2: Factor each term using the greatest common factor.

Let's go through each step:

Step 1: Recognize that both terms $8x^2$ and $4x$ contain $x$ as a common factor.
Moreover, the numerical coefficients 8 and 4 have a common factor of 4.

Step 2: Factor the expression:
- $8x^2$ can be expressed as $8 \cdot x \cdot x$ .
- $4x$ can be written as $4 \cdot x$ .

Bringing them together, we can rewrite the expression:

$8x^2 - 4x = 8 \cdot x \cdot x - 4 \cdot x$ .

Thus, the solution to the problem is $8\cdot x\cdot x-4\cdot x$ .

Final Answer

$8\cdot x\cdot x-4\cdot x$

Key Points to Remember

Essential concepts to master this topic

Rule: Break each term into its prime factors and variables
Technique: Write $8x^2$ as $8 \cdot x \cdot x$ and $4x$ as $4 \cdot x$
Check: Multiply back: $8 \cdot x \cdot x - 4 \cdot x = 8x^2 - 4x$ ✓

Common Mistakes

Avoid these frequent errors

Confusing basic components with complete factoring
Don't immediately factor out common terms like 4x(2x - 1) = wrong format! This gives the factored form, not basic components. Always break down each term into its individual factors: coefficients times individual variable 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's the difference between basic components and factoring?

Basic components means breaking each term into its individual parts. Factoring means pulling out common factors. For $8x^2 - 4x$ , basic components = $8 \cdot x \cdot x - 4 \cdot x$ , but factored form = $4x(2x - 1)$ .

Why write x twice in the first term?

Because $x^2$ means x times x! When showing basic components, we write out each factor separately: $x^2 = x \cdot x$ .

Do I need to show multiplication signs?

Yes! Basic components require showing all multiplication explicitly. Use $\cdot$ symbols between each factor to make it clear: $8 \cdot x \cdot x$ , not $8xx$ .

What if the coefficient is prime?

If the coefficient can't be factored further (like 7 or 11), just leave it as is. For example, $7x^3$ becomes $7 \cdot x \cdot x \cdot x$ .

How is this different from expanding?

Expanding means multiplying out brackets like $(x+2)(x+3)$ . Basic components means breaking down existing terms into their individual factors without any brackets.

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