(x+6)^2 Is this right? (x+6)^2 =36x

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(x+6)^2 Is this right? (x+6)^2 =36x

Mathematics
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im guessing you have to expand this...??
Not really sure if i do or not all they gave me was (x+6)^2?
Have you ever done problems that asked you "to expand" an expression?

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Nope.
Lets start from this. \(\large\color{black}{\rm \displaystyle expression\text{#}1(expression\text{#}2) }\) is same thing as \(\large \color{black}{\rm expression\text{#}1~\cdot~expression\text{#}2}\) you know that right?
? What is expression 1 and 2 suppose to mean?
any expreesions, i am just naming them like this.
this is equivalent to saying a(b) is same as saying a•b
Okay.
good.
So, if I say a(b), then I know that it is a•b and it would be the same thing as a•b.
(Just trying to get general way of writing things straight)
a(b) = a•b = ab
all 3 parts are same...
Alright
now, if I said: a(b+c), then what am I really doing? a(b+c) = a•(b+c) = a•b+a•c=ab+ac
I am multiplying everything inside the parenthesis times a.
is this making some sense?
Yeah, just not sure what this has to do with the problem i asked.
Anyone?
\(\large (x+6)^2 \implies (x+6)(x+6)\implies \begin{cases} x\cdot x\implies &?\\ x\cdot 6\implies &?\\ 6\cdot x\implies &?\\ 6\cdot 6\implies &? \end{cases}\)
Okay think i got it. x*x = X^2, x*6 = x^6, 6*x= 6x and 6*6 = 36
(x+6)^2 is the same as (x+6)*(x+6) squaring something means you're multiplying it by itself To expand out (x+6)*(x+6) you can use the FOIL rule but I like a table better because you can use a table for things that FOIL can't do |dw:1437695027927:dw|
To fill out the table, you multiply the headers example: x times x = x^2 |dw:1437695125576:dw|
yeah.
you said `x*x = X^2, x*6 = x^6, 6*x= 6x and 6*6 = 36` so this is reflected in the table |dw:1437695217158:dw|
The last thing to do is add up x^2, 6x, 6x, and 36 (all the terms found in the table). Combining like terms if any.
oh just noticed you wrote `x*6 = x^6` it should be x*6 = 6x
Okay.
Sooo?
what do you get when you add up x^2, 6x, 6x, and 36
48x^2
you can't combine 6x with 36 to get 42x
6x and 36 aren't like terms
12x^2
6x + 6x = ???
Were adding right? 12x^2
6 apples + 6 apples = ______ apples
the x doesn't become x^2 when you add 6x+6x
Oh, 6x+6x =12x
so we get x^2+12x+36
that's as far as we can go because there are no other like terms left to combine
Alright. Thanks @jim_thompson5910

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