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I see that you've uploaded an image containing math problems about polynomials. Let me transcribe and solve them for you:

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### 1. **Troba els coeficients de \( P(x) \cdot Q(x) + P(x) \cdot R(x) \) essent \( P(x) = 6x+1 \), \( Q(x) = 3x^2-2 \) i \( R(x) = x^2+14x \)**  
We need to calculate:  
\[ P(x) \cdot Q(x) + P(x) \cdot R(x) \]  

1. \( P(x) \cdot Q(x) = (6x+1)(3x^2-2) = 18x^3 - 12x + 3x^2 - 2 \)  
   Simplify:  
   \[ 18x^3 + 3x^2 - 12x - 2 \]

2. \( P(x) \cdot R(x) = (6x+1)(x^2+14x) = 6x^3 + 84x^2 + x^2 + 14x \)  
   Simplify:  
   \[ 6x^3 + 85x^2 + 14x \]

Add the two results:  
\[
(18x^3 + 3x^2 - 12x - 2) + (6x^3 + 85x^2 + 14x) = 24x^3 + 88x^2 + 2x - 2
\]

**Answer: Coefficients are \( 24, 88, 2, -2 \).**

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### 2. **Calcula el valor numèric de \( 2x^3 - 5x^2 + 4 \) en \( x = 2 \)**  

Substitute \( x = 2 \):  
\[
2(2^3) - 5(2^2) + 4 = 2(8) - 5(4) + 4 = 16 - 20 + 4 = 0
\]

**Answer: \( 0 \).**

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### 3. **Troba l'expressió algebraica que defineix l'àrea de 6 quadrats de costat \( x+y \) i 6 rectangles de base \( x \) i altura \( y \)**  

1. The area of one square is:  
   \[
   (x+y)^2 = x^2 + 2xy + y^2
   \]

   So, the total area of 6 squares:  
   \[
   6(x^2 + 2xy + y^2) = 6x^2 + 12xy + 6y^2
   \]

2. The area of one rectangle is:  
   \[
   x \cdot y = xy
   \]

   So, the total area of 6 rectangles:  
   \[
   6(xy) = 6xy
   \]

Add both areas:  
\[
6x^2 + 12xy + 6y^2 + 6xy = 6x^2 + 18xy + 6y^2
\]

**Answer: \( 6x^2 + 18xy + 6y^2 \).**

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### 4. **És certa la igualtat \( 9x^2 + 30x + 25 = (3x+5)^2 \)?**  

Expand \( (3x+5)^2 \):  
\[
(3x+5)^2 = 9x^2 + 30x + 25
\]

The left and right sides are identical, so **the equality is true**.

**Answer: Yes, it is true.**

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### 5. **Troba els coeficients de \( (2x+1)^2 \)**  

Expand \( (2x+1)^2 \):  
\[
(2x+1)^2 = (2x)(2x) + 2(2x)(1) + (1)(1) = 4x^2 + 4x + 1
\]

**Answer: Coefficients are \( 4, 4, 1 \).**

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Would you like detailed explanations or clarifications? 😊

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### Related Questions:
1. What happens if \( P(x) \) has more terms in problem 1?  
2. Can you calculate \( P(x) \cdot Q(x) \cdot R(x) \) for problem 1?  
3. How do you find coefficients for any polynomial expression?  
4. How is the expansion of \( (x+y)^2 \) related to the binomial theorem?  
5. Can we solve problem 4 with inequalities instead of expansion?

### Tip:
When multiplying polynomials, organize terms by degree to avoid errors in coefficients!

Find the coefficients and solve polynomial-related problems such as expansions, verifications, and simplifications.

Explore step-by-step solutions to polynomial problems, including multiplication, simplification, and coefficient calculations. Learn key algebraic techniques such as binomial expansion and the difference of squares. Suitable for Grade 8-10 students.

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