Find simpler expressions for $a-b$ and for $a+2b$ separately. Be careful with the minus sign in $a-b$ and with distributing the $2$ in $2b$.

After you have $(a-b)$ and $(a+2b)$ in simple binomial form, multiply them, then add $b$, and finally combine like terms (the $x^2$ terms, the $x$ terms, and the constants).

Once you have your simplified polynomial, match its $x^2$, $x$, and constant coefficients to the answer choices to see which one is equivalent.

In Desmos, type the expression with $a$ and $b$ substituted: f(x) = ((2x-5) - (x+3)) * ((2x-5) + 2*(x+3)) + (x+3). This is the function you want to match to an answer choice.

For each option A–D, create a new expression like g_A(x) = f(x) - (expression from option A), g_B(x) = f(x) - (expression from option B), and so on. Look at the graphs: the option for which the corresponding graph is a horizontal line on $y=0$ for all shown $x$ is the equivalent expression.

We are given $a=2x-5$ and $b=x+3$, and we want to simplify $(a-b)(a+2b)+b$.

Replace $a$ and $b$ with their expressions in terms of $x$:

First simplify $a-b$:

Then simplify $a+2b$:

So the expression becomes:

Now expand $(x-8)(4x+1)$ using distribution (FOIL):

4x^2 -31x -8 + (x+3).

Combine the $x$ terms and the constant terms:

So $(a-b)(a+2b)+b$ is equivalent to $4x^2 - 30x - 5$, which corresponds to choice A.