Rewrite the expression without parentheses by distributing the negative sign to each term of the second polynomial before combining anything.

After distribution, group $y^2$ terms together, $y$ terms together, and constant terms together, and then add their coefficients.

In Desmos, type f(y) = (4y^2 + 3y - 2) - (y^2 - 5y + 6) to define the original expression as a function.

Define four more functions, for example: A(y) = 5y^2 - 2y + 4, B(y) = 3y^2 - 2y + 8, C(y) = 3y^2 + 8y - 8, and D(y) = 3y^2 + 8y + 8.

Look at the graphs of $f(y)$ and each choice; the equivalent expression will have a graph that lies exactly on top of $f(y)$ for all visible $y$-values. You can also create a table for $f(y)$ and the choices at several $y$-values (like $-2,-1,0,1,2$); the matching expression will give the same outputs as $f(y)$ for every tested input.

Start with the given expression:

You are subtracting the entire second polynomial from the first, so the negative sign must apply to every term inside the second parentheses.

Distribute the minus sign to each term of the second polynomial:

• The $y^2$ becomes $-y^2$.
• The $-5y$ becomes $+5y$.
• The $+6$ becomes $-6$.

So the expression becomes:

Group like terms:

• $y^2$ terms: $4y^2 - y^2$
• $y$ terms: $3y + 5y$
• Constant terms: $-2 - 6$

Now combine:

• $4y^2 - y^2 = 3y^2$
• $3y + 5y = 8y$
• $-2 - 6 = -8$

Putting the combined terms together, the simplified expression is:

This matches answer choice C, so $3y^2 + 8y - 8$ is equivalent to the original expression.