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ANSWER

D.

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

EXPLANATION

We want to find the expression which is a square of a binomial.

In other words, we want to identify the expression which is a perfect square trinomial.

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

This expression can be rewritten as,

[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} [/tex]

This is a perfect square trinomial that can be factored as:

[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} = (4x + 3y) ^{2} [/tex]

This is the square of a binomial.

The correct answer is D

mixter17

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!

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