Remember the entire second product is being subtracted. After you expand both products, put parentheses around the second one and distribute the minus sign to each of its terms.

Once you have a single simplified expression, identify the term that has just $x$ (not $x^2$ and not the constant). Its coefficient is the value of $b$.

In Desmos (graphing or scientific), type the entire expression exactly as given: (4x - 11)(9x + 2) - (5x + 13)(7x - 6).

Use Desmos’s simplify/expand feature (for example, on the scientific calculator, press the = button) so it outputs the equivalent polynomial in standard form $ax^2 + bx + c$.

From the simplified polynomial that Desmos shows, locate the term with just $x$ and note its coefficient; that value is $b$.

Use distribution (FOIL) on $(4x - 11)(9x + 2)$:

• First: $4x \cdot 9x = 36x^2$
• Outer: $4x \cdot 2 = 8x$
• Inner: $-11 \cdot 9x = -99x$
• Last: $-11 \cdot 2 = -22$

Combine like terms in the middle:

So $(4x - 11)(9x + 2)$ becomes $36x^2 - 91x - 22$.

Now expand $(5x + 13)(7x - 6)$ in the same way:

• First: $5x \cdot 7x = 35x^2$
• Outer: $5x \cdot (-6) = -30x$
• Inner: $13 \cdot 7x = 91x$
• Last: $13 \cdot (-6) = -78$

Combine like terms in the middle:

So $(5x + 13)(7x - 6)$ becomes $35x^2 + 61x - 78$.

The original expression is

Substitute the expanded forms:

Distribute the minus sign across the second parentheses:

Now combine like terms:

• For $x^2$ terms: $36x^2 - 35x^2 = x^2$
• For $x$ terms: $-91x - 61x = -152x$
• For constants: $-22 + 78 = 56$

From the combined terms, the simplified expression is

This matches $ax^2 + bx + c$ with $a = 1$, $b = -152$, and $c = 56$. The question asks for $b$, so the value of $b$ is $-152$.