Answer:
[tex]16x^{2}y^{2}-24xyz+9z^2[/tex]
It is a perfect square trinomial.
Step-by-step explanation:
The square of a binomial can be solved like this:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
We have the expression:
[tex](4xy-3z)^2[/tex]
Then, we consider a and b as:
[tex]a=4xy\\ b=-3z[/tex]
The solution would be:
[tex]a^2=(4xy)^2=4^2x^2y^2=16x^2y^2[/tex]
[tex]b^2=(-3z)^2=(-3)^2z^2=9z^2[/tex]
[tex]2ab=2(4xy)(-3z)=-24xyz[/tex]
[tex](4xy-3z)^2=16x^2y^2-24xyz+9z^2 [/tex]
The required f(x) is equivalent to the difference of the square f(x) = [tex]= 16x^{2} y^{2} + 9z^{2} - 24xyz[/tex].
Given that,
Function f(x) = 4xy - 3z
We have to find,
f(x) is equivalent squared and which type of product.
According to the question,
A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself.
The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials.
Then, f(x) = (4xy - 3z)
[tex]= (4xy- 3z)^{2} \\ = (4xy-3z)(4xy-3z)\\= 4xy(4xy-3z)-3z(4xy-3z) \\= 16x^{2} y^{2} - 12xyz-12xyz+9z^{2} \\= 16x^{2} y^{2} + 9z^{2} - 24xyz[/tex]
The difference of the square f(x) = [tex]= 16x^{2} y^{2} + 9z^{2} - 24xyz[/tex].
Hence, The required f(x) is equivalent to the difference of the square f(x) = [tex]= 16x^{2} y^{2} + 9z^{2} - 24xyz[/tex].
For the more information about Perfect Square click the link given below.
https://brainly.com/question/2263981
