Diketahui f(x) = 2x + 3 maka [f(x)] ^ 2 - 3f(x + 1) =***

(A) 4x ^ 2 + 6x - 6

(B) 4x ^ 2 + 6x - 9

(C) 4x ^ 2 + 6x + 18

(D) 4x ^ 2 - 6x + 6

(E) 4x ^ 2 + 6x + 9

Let's solve the given expression step by step.

Given:  
\( f(x) = 2x + 3 \)

We need to find the value of:

\[
[f(x)]^2 - 3f(x + 1)
\]

### Step 1: Calculate \( [f(x)]^2 \)
\[
f(x) = 2x + 3
\]
\[
[f(x)]^2 = (2x + 3)^2
\]
Expanding \( (2x + 3)^2 \):
\[
[f(x)]^2 = (2x + 3)(2x + 3) = 4x^2 + 12x + 9
\]

### Step 2: Calculate \( f(x + 1) \)
Substitute \( x + 1 \) into the function \( f(x) \):
\[
f(x + 1) = 2(x + 1) + 3 = 2x + 2 + 3 = 2x + 5
\]

### Step 3: Calculate \( -3f(x + 1) \)
\[
-3f(x + 1) = -3(2x + 5) = -6x - 15
\]

### Step 4: Combine the results
Now, combine the expressions from Step 1 and Step 3:
\[
[f(x)]^2 - 3f(x + 1) = (4x^2 + 12x + 9) + (-6x - 15)
\]
\[
= 4x^2 + 12x - 6x + 9 - 15
\]
\[
= 4x^2 + 6x - 6
\]

### Final Answer
The correct answer is:

**(A) \( 4x^2 + 6x - 6 \)**

Would you like further details or have any questions?

Here are five related questions to explore:

1. How do you find the derivative of the function \( f(x) = 2x + 3 \)?
2. What is the general form of a quadratic equation?
3. How do you expand the square of a binomial, such as \( (ax + b)^2 \)?
4. How would the expression change if \( f(x) = 3x + 4 \)?
5. What are the steps to simplify an expression with multiple terms?

**Tip:** When expanding binomials, remember to apply the distributive property carefully to ensure all terms are accounted for.

Diketahui f(x) = 2x + 3 maka [f(x)] ^ 2 - 3f(x + 1) = ***

Learn how to solve the function expression [f(x)]^2 - 3f(x + 1), where f(x) = 2x + 3, with a detailed step-by-step solution. This algebra problem involves expanding binomials and applying the distributive property. Ideal for students in Grades 9-11.

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