6

$$9(x+2)^2 = 3^2(x+2)^2=(3(x+2))^2=(3x+6)^2$$

I want to know if the use of brackets in this problem has been done correctly. What is this method called?

Blue
  • 75,673
ilove cupcakes
  • 105
  • 1
  • 7
  • 2
    Notice I edited your question to improve the formatting. It is strongly advised that you use Mathjax to format your questions on this site - it's like LaTeX for the web. I edited your question this time since you are new, but in future, please format the question yourself. See here for a quick guide: MathJax tutorial – 5xum Dec 16 '21 at 08:28
  • 1
    Yes, this is correct. You can verify that also by evaluating your "starting term" and your "result", to check if this is indeed equal, if you are in doubt. – Cornman Dec 16 '21 at 08:30
  • 3
    The "method" is just the fact that the product of two squares is the square of its factors. – Michael Hoppe Dec 16 '21 at 20:19
  • 2
    You just used the rule $a^2\cdot b^2=(ab)^2$ , which is written out : $aabb=abab$ which holds in every commutative group or ring. – Peter Dec 20 '21 at 11:06
  • you should rephrase the sentence : which holds in every commutative group or ring. i understand what commutative means but maybe it's my English that is bad I don't know... please rephrase it. – ilove cupcakes Dec 29 '21 at 12:39

1 Answers1

4

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.

5xum
  • 123,496
  • 6
  • 128
  • 204