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

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 $24, 88, 2, -2$.

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: $0$.

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: $6x^2 + 18xy + 6y^2$.

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.

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 $4, 4, 1$.

Would you like detailed explanations or clarifications? 😊

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!