which is equivalent to $(4xy - 3z)^2$, and what type of special product is it?\n1. $16x^{2}y^{2}+9z^{2}$…

which is equivalent to $(4xy - 3z)^2$, and what type of special product is it?\n1. $16x^{2}y^{2}+9z^{2}$, the difference of squares\n2. $16x^{2}y^{2}+9z^{2}$, a perfect square trinomial\n3. $16x^{2}y^{2}-24xyz + 9z^{2}$, the difference of squares\n4. $16x^{2}y^{2}-24xyz + 9z^{2}$, a perfect square trinomial

which is equivalent to $(4xy - 3z)^2$, and what type of special product is it?\n1. $16x^{2}y^{2}+9z^{2}$, the difference of squares\n2. $16x^{2}y^{2}+9z^{2}$, a perfect square trinomial\n3. $16x^{2}y^{2}-24xyz + 9z^{2}$, the difference of squares\n4. $16x^{2}y^{2}-24xyz + 9z^{2}$, a perfect square trinomial

Answer

Explanation:

Step1: Recall the formula

The formula for $(a - b)^2$ is $a^{2}-2ab + b^{2}$. Here $a = 4xy$ and $b=3z$.

Step2: Calculate $a^{2}$

$(4xy)^{2}=4^{2}x^{2}y^{2}=16x^{2}y^{2}$.

Step3: Calculate $2ab$

$2\times(4xy)\times(3z)=24xyz$.

Step4: Calculate $b^{2}$

$(3z)^{2}=9z^{2}$.

Step5: Find $(4xy - 3z)^{2}$

$(4xy - 3z)^{2}=(4xy)^{2}-2\times(4xy)\times(3z)+(3z)^{2}=16x^{2}y^{2}-24xyz + 9z^{2}$.

Step6: Identify the special - product type

The expression $16x^{2}y^{2}-24xyz + 9z^{2}$ is in the form of $a^{2}-2ab + b^{2}$, which is a perfect - square trinomial.

Answer:

D. $16x^{2}y^{2}-24xyz + 9z^{2}$, a perfect square trinomial