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Problem 4 Hard Difficulty

$$9 a^{4}+12 a^{2} b^{2}+4 b^{4}$$
Which of the following is equivalent to the expression shown above?
\begin{array}{l}{\text { A) }\left(3 a^{2}+2 b^{2}\right)^{2}} \\ {\text { B) }(3 a+2 b)^{4}} \\ {\text { C) }\left(9 a^{2}+4 b^{2}\right)^{2}} \\ {\text { D) }(9 a+4 b)^{4}}\end{array}


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Video Transcript

king. So for this one, we see from our answer choices that we do eventually want to figure out how to factor the above the equation. So if you want a factor it we also have to realize that all of these are perfect squares, which means it's not like a two factors that are different. It's going to be two of the same exact thing. So then we know that for a perfect square, a sum of squares we know it's going to be exposed. Y squared must be written in the form of X squared plus two x y plus y squared. So in order to get this back into their all we really have to do is take this first and the last to the X squared in the Y Square vice just square with them and then put it into the Prentice's and square. So if we want to do that, we know that this is our acts, value our X square value, and then this is our Y square value. So if we square written nine eight the fourth we get three a squared to then if we square it the four B to the fourth, we get to be squared so clearly we can put that put these into our ex and r y and get three a squared plus two b squared, the whole quantity squared. That's gonna be a