write 2x+0.8x-0.04x in the form A-B(x+Csquared) where a, b and c are constants

To express \( 2x + 0.8x - 0.04x \) in the form \( A - B(x + C^2) \), let's follow a step-by-step process.

### Step 1: Simplify the given expression
We can combine the like terms:
\[
2x + 0.8x - 0.04x = (2 + 0.8 - 0.04)x = 2.76x
\]

So, the simplified expression is:
\[
2.76x
\]

### Step 2: Write it in the desired form
We need to express it in the form \( A - B(x + C^2) \). To do that, let's interpret this:

- The term \( B(x + C^2) \) should contain \( x \) somewhere, which suggests \( B = 0 \) (since \( x \) should only be in a linear form like \( A - B(x + C^2) \)).

Thus, the expression simplifies to just \( A = 2.76 \), and the rest of the terms vanish:
\[
2.76x = 2.76 - 0(x + C^2)
\]

So the constants are:
- \( A = 2.76 \)
- \( B = 0 \)
- \( C \) can be any number, as it does not affect the form.

Hence, the final form is:
\[
2.76 - 0(x + C^2)
\]

This represents the expression in the form \( A - B(x + C^2) \) where \( A = 2.76 \), \( B = 0 \), and \( C \) is arbitrary.

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Do you want more details or have any further questions?

Here are 5 related questions:
1. How do you expand expressions like \( A - B(x + C^2) \)?
2. What are the properties of linear equations when simplified?
3. How do you simplify complex expressions involving multiple constants and variables?
4. How does the value of constants affect the overall structure of an equation?
5. Can this form \( A - B(x + C^2) \) represent a wider range of expressions?

**Tip**: Always combine like terms first to simplify algebraic expressions efficiently.

Discover how to simplify the linear expression 2x + 0.8x - 0.04x into the form A - B(x + C^2). This step-by-step solution covers core algebraic concepts like combining like terms and expressing results in specific forms. Suitable for students in Grades 8-10.

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