After expanding, rewrite the whole expression in terms of $x^2$ terms, $x$ terms, and constants, then add the coefficients of like terms.

Once you have the simplified expression, compare it to the form $ax^2 + bx + 5$ and identify the values of $a$ and $b$ from the coefficients of $x^2$ and $x$.

After finding $a$ and $b$, remember the question is asking for $a + b$, not for $a$ or $b$ individually.

In a Desmos input line, type the full expression: $(7x^2 - 2x + 5) + 3(4x - x^2)$.

In a new line, type expand((7x^2 - 2x + 5) + 3(4x - x^2)). Desmos will show the simplified polynomial, from which you can read off the coefficients of $x^2$ and $x$ (these are $a$ and $b$).

Take the coefficient of $x^2$ (your $a$) and the coefficient of $x$ (your $b$) from the expanded form in Desmos, then add those two numbers to find $a + b$.

Start by expanding the expression $3(4x - x^2)$.

Multiply each term inside by 3:

Now rewrite the whole expression using this result:

Combine the $x^2$ terms, the $x$ terms, and the constant terms.

First, group like terms:

Now combine:

• $7x^2 - 3x^2 = 4x^2$
• $-2x + 12x = 10x$
• The constant term stays $5$

So the simplified expression is:

The problem says the expression is equivalent to $ax^2 + bx + 5$.

From the simplified form

you can match term by term:

• The coefficient of $x^2$ is $4$, so $a = 4$.
• The coefficient of $x$ is $10$, so $b = 10$.
• The constant term is $5$, which already matches.

The question asks for $a + b$.

You found $a = 4$ and $b = 10$, so

So, the value of $a + b$ is 14.