After expanding the square, distribute the $5$ over $(y + 2)$ and then distribute the negative sign over $(y^2 - 16)$. What happens to each term inside the last parentheses when you subtract the whole expression?

Once everything is expanded, collect all $y^2$ terms together, all $y$ terms together, and all constant terms together before combining them.

If you’re unsure, plug in an easy value (like $y = 1$ or $y = 2$) into the original expression and each answer choice to see which one always matches.

In the first expression line, type (3y - 4)^2 + 5(y + 2) - (y^2 - 16). Desmos will treat y as the variable.

On new lines, enter each option:

• 8y^2 - 29y + 42
• 8y^2 - 19y + 26
• 7y^2 - 19y + 42
• 8y^2 - 19y + 42 Desmos will graph each of these as a function of $y$ (you can think of the horizontal axis as $y$ instead of $x$).

Zoom out if needed so you can see several curves. The correct option is the one whose graph lies exactly on top of the graph of the original expression for all visible values. Alternatively, tap the dots next to the expressions, create a table for the original expression and for each option, and compare the numeric outputs at several $y$-values; the correct choice will match the original expression’s values every time.

First expand $(3y - 4)^2$.

Use the pattern $(a - b)^2 = a^2 - 2ab + b^2$ with $a = 3y$ and $b = 4$:

So the original expression becomes:

Now expand $5(y + 2)$ and distribute the minus sign across $(y^2 - 16)$.

• For $5(y + 2)$:

• For $-(y^2 - 16)$, think of multiplying by $-1$:

Substitute these into the expression:

Group and combine like terms: $y^2$ terms, $y$ terms, and constants.

• $y^2$ terms: $9y^2 + (-y^2) = 8y^2$
• $y$ terms: $-24y + 5y = -19y$
• Constant terms: $16 + 10 + 16 = 42$

So the entire expression simplifies to

which matches choice D.