Hello!
The answer is:
D) [tex]16x^{2} +24xy+9y^{2}[/tex]
Why?
We are looking for an expression that satisfies the perfect square trinomial form, which can be defined by the following notable product:
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]
From the given options, we can see that the only option that matches with the perfect square trinomial form is:
[tex]16x^{2} +24xy+9y^{2}[/tex]
We can rewrite the expression by the following way:
[tex](4x+3y)^{2}[/tex]
If we square the binomial, we will have the perfect square binomial expression given from the options.
So, squaring, we have:
[tex](4x+3y)^{2}=(4x)^{2}+2*(4x*3y)+(3y)^{2}\\\\(4x+3y)^{2}=16x^{2} +24xy+9y^{2}[/tex]
Hence, the answer is:
D) [tex]16x^{2} +24xy+9y^{2}[/tex]
Have a nice day!
