Amanita, let's carefully solve the problem step by step. The task is to write certain phrases as mathematical expressions. Let's focus on part (a) as you requested, but I will also explain the context from the image for clarity.

Step-by-Step Plan:

1. Understand the Phrase:
   The phrase "квадрат разности 2x и 5y" translates to "the square of the difference of $2x$ and $5y$" in English.

2. Write the Difference:
   The difference of $2x$ and $5y$ is written as $2x - 5y$.

3. Square the Difference:
   To find the square of this difference, we need to raise the expression to the power of 2: $(2x - 5y)^2$.

4. Expand the Expression (Optional):
   If required, we can expand $(2x - 5y)^2$ using the formula $(a - b)^2 = a^2 - 2ab + b^2$.

Let's execute these steps:

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Step 1: Write the Difference

The difference between $2x$ and $5y$ is:

$$2x - 5y$$

Step 2: Square the Difference

The square of the difference is:

$$(2x - 5y)^2$$

Step 3: Expand the Expression

Let's expand $(2x - 5y)^2$ using the formula $(a - b)^2 = a^2 - 2ab + b^2$:

Let $a = 2x$ and $b = 5y$:

$(2x - 5y)^2 = (2x)^2 - 2 \cdot 2x \cdot 5y + (5y)^2$

Now, let's calculate each term:

• $(2x)^2 = 4x^2$
• $-2 \cdot 2x \cdot 5y = -20xy$
• $(5y)^2 = 25y^2$

So, the expanded form is:

$(2x - 5y)^2 = 4x^2 - 20xy + 25y^2$

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Final Answer

The square of the difference of $2x$ and $5y$ is:

$$(2x - 5y)^2$$

or, in expanded form:

$4x^2 - 20xy + 25y^2$

Amanita, let me know if you want to work on parts (b) or (c) as well, or if you need further explanation!