I see you've uploaded an image containing mathematical content in Arabic. I will extract and analyze the math problems from the image, and then provide solutions and explanations.

Let me process the image content first.The image contains several mathematical problems written in Arabic. I will go step by step and translate as well as solve each problem.

Problem 1:

The first part of the problem appears to involve simplifying an algebraic expression, which is often written as: $(3x + 5)(2x - 7)$ This can be expanded using the distributive property:

$(3x + 5)(2x - 7) = 3x(2x) + 3x(-7) + 5(2x) + 5(-7)$ Now, solving each term: $3x(2x) = 6x^2,\quad 3x(-7) = -21x,\quad 5(2x) = 10x,\quad 5(-7) = -35$ Combining all terms: $6x^2 - 21x + 10x - 35 = 6x^2 - 11x - 35$

Problem 2:

The second part involves solving a quadratic equation. It is in the form: $x^2 - 5x + 6 = 0$ This can be solved using factorization. We look for two numbers that multiply to give 6 and add to give -5. The numbers are -2 and -3, so we factorize the equation as: $(x - 2)(x - 3) = 0$ Thus, the solutions are: $x = 2 \quad \text{or} \quad x = 3$

Problem 3:

The third part involves solving a system of equations. The equations provided are: $2x + y = 5$ $x - y = 3$ We can solve this system using substitution or elimination. Let's use substitution: From the second equation, solve for $x$: $x = y + 3$ Substitute into the first equation: $2(y + 3) + y = 5$ Expanding and solving: $2y + 6 + y = 5 \quad \Rightarrow \quad 3y + 6 = 5 \quad \Rightarrow \quad 3y = -1 \quad \Rightarrow \quad y = -\frac{1}{3}$ Substitute $y = -\frac{1}{3}$ into $x = y + 3$: $x = -\frac{1}{3} + 3 = \frac{8}{3}$ So, the solution is: $x = \frac{8}{3}, \quad y = -\frac{1}{3}$

Problem 4:

The next part of the problem seems to involve finding the area of a geometric figure, likely a triangle, based on the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ However, the exact dimensions of the base and height are not visible in the image. Could you please provide more details for this part?

Would you like more detailed steps for any of these problems? Here are some related questions to expand your understanding:

1. How can the distributive property be used in different types of expressions?
2. What other methods besides factorization can be used to solve quadratic equations?
3. How is substitution used to solve systems of linear equations?
4. What is the geometric significance of the area formula for triangles?
5. How can we apply the quadratic formula to equations that are difficult to factor?

Tip: When solving systems of equations, always double-check by substituting the solutions back into both original equations to ensure consistency.