Question

Which is equivalent to (4xy – 3z)2, and what type of special product is it?

16x2y2 + 9z2, the difference of squares

16x2y2 + 9z2, a perfect square trinomial

16x2y2 – 24xyz + 9z2, the difference of squares

16x2y2 – 24xyz + 9z2, a perfect square trinomial

Answer 1

`(4xy-3z)^(2) =(4xy)^(2) -2(4xy)(3z)+ (3z)^(2) =16 x^(2) y^(2) -24xyz+9 z^(2)`
The type of special product is 'a perfect square trinomial'.

Answer 2

`16x^2y^2-24xyz+9z^2`

It is a perfect square trinomial.

Explanation:

The given expression is
`(4xy-3z)^2`

We can use the formula
`(a-b)^=a^2-2ab+b^2`

Here, we have

a = 4xy, b = 3z

Using the formula, we have

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

Therefore, the equivalent expression is
`16x^2y^2-24xyz+9z^2`

It is a perfect square trinomial.