<s>[INST] How to simplify an expression that does not have a common factor I am trying to simplify this expression :
$$9a^4 + 12a^2b^2 + 4b^4$$
So I ended up having this :
$$(3a^2)^2 + 2(3a^2)(2b^2) + (2b^2)^2$$
However, after that I don't know how to keep on simplifying the equation, it is explained that the answer is $(3a^2 + 2b^2)^2$ because the expression is equivalent to $(x + y)^2$ but I don't understand how they get to that ?
 [/INST] Using the following formula.
$x^2 + 2xy + y^2 = (x+y)^2$
Here $x = 3a^2$, $y = 2b^2$
On putting values in left hand side of above formula.
$(3a^2)^2+2(3a^2)(2b^2)+(2b^2)^2 = 9a^4+12a^2b^2+4b^4 = (3a^2+2b^2)^2$
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