Now expand $(6x - 3y)(x + y)$ the same way: multiply each term in the first parentheses by each term in the second.

Once both products are expanded, remember that the minus sign applies to every term in the second product. Put the second product in parentheses and distribute the negative sign before combining like terms.

In Desmos, create sliders for $x$ and $y$ (for example, set $x=1$ and $y=2$), then type the original expression (3x+5)(2x-y)-(6x-3y)(x+y) on a line and note the resulting numerical value.

On separate lines, type each answer choice expression using the same $x$ and $y$ values (for example, 3y^2-6xy+10x-5y, 3y^2-6xy-10x-5y, etc.) and compare their numerical outputs to the value from the original expression.

Change the slider values for $x$ and $y$ to a few different pairs (such as $x=-2, y=3$ or $x=0, y=-1$) and re-check. The expression that matches the original expression’s value for all tested $(x,y)$ pairs is the equivalent one.

Use the distributive property (FOIL) on $(3x + 5)(2x - y)$.

So the first product simplifies to $6x^2 - 3xy + 10x - 5y$.

Now expand $(6x - 3y)(x + y)$.

So the second product simplifies to $6x^2 + 3xy - 3y^2$.

Rewrite the full expression by substituting the expanded forms and carefully keeping parentheses:

Distribute the minus sign to every term in the second parentheses:

Group and combine like terms:

• $6x^2 - 6x^2 = 0$
• $-3xy - 3xy = -6xy$
• The $x$ term is $+10x$
• The $y$ term is $-5y$
• The $y^2$ term is $+3y^2$

So the entire expression simplifies to

This matches answer choice A.