Question

Which is equivalent to (4xy-3x)^2, and what type of special product is it?

Answer 1

The correct option is 4.

Explanation:

The given expression is

`(4xy-3z)^2`

Algebraic formula:

`(a-b)^2=a^2-2ab+b^2`

It is a perfect square trinomial.

Using algebraic formula, we get

`(4xy-3z)^2=(4xy)^2-2(4xy)(3z)+(3z)^2`

`(4xy-3z)^2=16x^2y^2-24xyz+9z^2`

Therefore option 4 is correct.

Answer 2

It's not the difference of squares, rather it is the square of a difference. That leaves a perfect square trinomial, which narrows your selection to two choices. An expression with 2 terms is not a trinomial, so that further narrows your selection. The appropriate choice is

... (4xy -3z)² = 16x²y² -24xyz +9z², a perfect square trinomial

_____

The expression you have in your problem statement has no z term, so none of the choices is applicable to that one.