For $(2x + 5y)^2$, recall the pattern $(a + b)^2 = a^2 + 2ab + b^2$. Identify $a$ and $b$, then expand.

After expanding $(x - y)(3x + 11y)$, remember that the whole result is being subtracted. Distribute the negative sign to each term before combining like terms.

In Desmos, first set a value for $y$, for example type y = 2. Then on the next line, type the original expression as a function of $x$, such as f(x) = (2x + 5y)^2 - (x - y)(3x + 11y).

On new lines, enter each choice (using the same fixed value of $y$) as functions, for example g(x) = x^2 + 12x*y + 36y^2, h(x) = x^2 + 12x*y - 36y^2, etc. Use a table or the graph to compare these to $f(x)$.

Check which choice’s function has exactly the same graph or the same table values as $f(x)$ for many $x$-values. The choice whose expression always matches the original expression is the correct answer.

First expand $(2x + 5y)^2$ using the pattern $(a + b)^2 = a^2 + 2ab + b^2$.

So the first part becomes $4x^2 + 20xy + 25y^2$.

Now expand $(x - y)(3x + 11y)$ by distributing each term in the first parentheses over the second.

So the second part is $3x^2 + 8xy - 11y^2$.

The original expression is

Substitute the expanded forms:

Be careful: the minus sign applies to every term inside the parentheses.

Distribute the negative sign across the second parentheses:

Now combine like terms:

• For $x^2$: $4x^2 - 3x^2 = x^2$.
• For $xy$: $20xy - 8xy = 12xy$.
• For $y^2$: $25y^2 + 11y^2 = 36y^2$.

So the simplified expression is

which matches answer choice A.