Answer:
the right answer is [tex]4(4x-3)^{2}[/tex]
Step-by-step explanation:
First of all, we need to rewrite the entire trinomial, for that we can see that all the numbers "64, 96 and 36" are multiplies or 4. So using the 4 as a common factor we have:
[tex]4(16x^{2}-24x+9)[/tex] using parentheses to know that 4 is a common factor.
now working into the parentheses "[tex](16x^{2} -24x+9)[/tex]" we can appreciate that is a perfect square trinomial.
but we need to prove that is a perfect square trinomial, so fro that we need to take the square root to the first and third terms; in this example "[tex]16x^{2}[/tex] " is the first term "[tex]24x[/tex]" the second term and "9" the third term; the first term and third term always need to be positive.
so, the square root for [tex]x^{2}[/tex] is:
[tex]\sqrt{16x^{2} }=4x[/tex]
and the square root for 9 is
[tex]\sqrt{9}=3[/tex].
now the last step is to take the squares roots and multiplying them with -2 (in theory to be a perfect square trinomial the second term need to be equal to two times the square root of the first and third term, here the second term is negative, that's why we multiply with -2.)
so we have
[tex]2*16x*3= 24x[/tex], and [tex]24x[/tex] it's indeed the second term, so it is a perfect square trinomial.
so now we can use the next formula: [tex]a^{2}-2ab+b^{2}[/tex]
and we know already that a=4x and b=3 (they're the result of the square root of the first and third term)
replacing:
[tex](4x-3)^{2}[/tex]
and now adding the 4 of the common factor we have:
[tex]4(4x-3)^{2}[/tex]
