<s>[INST] Is my work transforming $9(x+2)^2$ to $(3x+6)^2$ correct? What is this method called? $$9(x+2)^2 = 3^2(x+2)^2=(3(x+2))^2=(3x+6)^2$$
I want to know if the use of brackets in this problem has been done correctly. What is this method called?
 [/INST] Yes, all steps are correct.
You can also verify that the result is correct by expanding both expressions.
The first expression expands out to
$$9(x+2)^2=9(x^2+2\cdot 2\cdot x+2^2)=9(x^2+4x+4)=9x^2+36x+36$$
while the final expression expands out to
$$(3x+6)^2=(3x)^2+2\cdot(3x)\cdot 6 + 6^2 = 3^2x^2+2\cdot3\cdot6\cdot x + 36=9x^2+36x+36$$
The two expansions match, confirming the original expressions are equivalent.
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