After you expand both products, remember that you are subtracting the entire second expression, not just its first term. How does this affect each term inside the second parentheses?

Once you write the subtraction without parentheses, group the $x^2$ terms, the $x$ terms, and the constants, and then simplify each group.

Type the expression (3x-2)(x+5) - (x-1)(2x+7) into a line in Desmos; this defines a function of $x$ (you can name it f(x) if you like).

On new lines, enter each option as its own function, for example g(x) = x^2 + 8x + 3, h(x) = x^2 + 18x - 3, etc. Look at the graphs: the correct choice will be the one whose graph lies exactly on top of the graph of the original expression for all visible $x$ values.

Create a table for the original expression and for one choice at a time (click the gear icon and select "Table"). Plug in several $x$-values (like $-2, 0, 1, 3$) and see whether the outputs match for every value; the matching one is the equivalent expression.

You are given

To find an equivalent expression, expand each product (multiply out the parentheses) and then simplify the result by combining like terms.

Use distribution (FOIL) on $(3x-2)(x+5)$:

• First: $3x \cdot x = 3x^2$
• Outer: $3x \cdot 5 = 15x$
• Inner: $-2 \cdot x = -2x$
• Last: $-2 \cdot 5 = -10$

Add these together:

Now expand $(x-1)(2x+7)$:

• First: $x \cdot 2x = 2x^2$
• Outer: $x \cdot 7 = 7x$
• Inner: $-1 \cdot 2x = -2x$
• Last: $-1 \cdot 7 = -7$

Add these together:

So the whole expression becomes

Subtract each term in the second parentheses from the corresponding term in the first:

Simplify:

• $3x^2 - 2x^2 = x^2$
• $13x - 5x = 8x$
• $-10 - (-7) = -10 + 7 = -3$

So the expression simplifies to

which is the equivalent expression.