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A perfect square trinomial is found in the expression where both the leading coefficients and the constant are both perfect squares. That only is the case with the third choice above. 16 is a perfect square of 4 times 4, and 9 is a perfect square of 3 times 3. We need to set it up into its perfect square factors and FOIL to make sure, so let's do that. Not only is 16 a perfect square in that first term, but so is x-squared. Not only is 9 a perfect square in the third term, but so is y-squared. So our factors will look like this:

(4x + 3y)(4x + 3y). FOIL that out to see that it does in fact give you back the polynomial that is the third choice down.

Answer:

C. [tex]16x^2+24xy+9y^2[/tex]

Step-by-step explanation:

We have been given 4 expressions and we are asked to choose the expression that is a perfect square trinomial.

We know that a perfect square trinomial is in form: [tex]a^2+2ab+b^2[/tex].

Upon looking at our given choices we can see that option C is the correct choice as we can write as:

[tex]16x^2+24xy+9y^2=(4x)^2+2(4x\cdot 3y)+(3y)^2[/tex]

[tex]16x^2+24xy+9y^2=(4x)^2+2(12xy)+(3y)^2[/tex]

[tex]16x^2+24xy+9y^2=(4x)^2+24xy+(3y)^2[/tex]

Therefore, option C is the correct choice.

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