Question

Which is equivalent to (4 x y minus 3 z) squared, and what type of special product is it?

16 x squared y squared + 9 z squared, the difference of squares

16 x squared y squared + 9 z squared, a perfect square trinomial

16 x squared y squared minus 24 x y z + 9 z squared, the difference of squares

16 x squared y squared minus 24 x y z + 9 z squared, a perfect square trinomial

Answer 1

The expression (4xy - 3z)^2 is equivalent to 16x^2y^2 - 24xyz + 9z^2, and it is a perfect square trinomial.

Step-by-step explanation:

The expression (4xy - 3z)2 is a perfect square trinomial. To square this expression, each term inside the parentheses is squared individually, then all terms are combined to form the final expression.

Squaring (4xy - 3z) gives:

(4xy - 3z)2 = (4xy)2 - 2(4xy)(3z) + (3z)2 = 16x2y2 - 24xyz + 9z2

Therefore, the equivalent expression is 16x2y2 - 24xyz + 9z2 and it is a perfect square trinomial.

Answer 2

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

It is a perfect square trinomial.

Step-by-step explanation:

The square of a binomial can be solved like this:

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

We have the expression:

`(4xy-3z)^2`

Then, we consider a and b as:

`a=4xy\\ b=-3z`

The solution would be:

`a^2=(4xy)^2=4^2x^2y^2=16x^2y^2`

`b^2=(-3z)^2=(-3)^2z^2=9z^2`

`2ab=2(4xy)(-3z)=-24xyz`

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