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

- anonymous

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

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- LynFran

im guessing you have to expand this...??

- anonymous

Not really sure if i do or not all they gave me was (x+6)^2?

- SolomonZelman

Have you ever done problems that asked you "to expand" an expression?

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## More answers

- anonymous

Nope.

- SolomonZelman

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?

- anonymous

? What is expression 1 and 2 suppose to mean?

- SolomonZelman

any expreesions, i am just naming them like this.

- SolomonZelman

this is equivalent to saying
a(b) is same as saying a•b

- anonymous

Okay.

- SolomonZelman

good.

- SolomonZelman

So, if I say
a(b), then I know that it is a•b and it would be the same thing as a•b.

- SolomonZelman

(Just trying to get general way of writing things straight)

- SolomonZelman

a(b) = a•b = ab

- SolomonZelman

all 3 parts are same...

- anonymous

Alright

- SolomonZelman

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

- SolomonZelman

I am multiplying everything inside the parenthesis times a.

- SolomonZelman

is this making some sense?

- anonymous

Yeah, just not sure what this has to do with the problem i asked.

- anonymous

@SolomonZelman

- anonymous

Anyone?

- jdoe0001

\(\large (x+6)^2 \implies (x+6)(x+6)\implies
\begin{cases}
x\cdot x\implies &?\\
x\cdot 6\implies &?\\
6\cdot x\implies &?\\
6\cdot 6\implies &?
\end{cases}\)

- anonymous

Okay think i got it. x*x = X^2, x*6 = x^6, 6*x= 6x and 6*6 = 36

- jim_thompson5910

(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|

- jim_thompson5910

To fill out the table, you multiply the headers
example: x times x = x^2
|dw:1437695125576:dw|

- anonymous

yeah.

- jim_thompson5910

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|

- jim_thompson5910

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.

- jim_thompson5910

oh just noticed you wrote `x*6 = x^6`
it should be x*6 = 6x

- anonymous

Okay.

- anonymous

Sooo?

- jim_thompson5910

what do you get when you add up x^2, 6x, 6x, and 36

- anonymous

48x^2

- jim_thompson5910

you can't combine 6x with 36 to get 42x

- jim_thompson5910

6x and 36 aren't like terms

- anonymous

12x^2

- jim_thompson5910

6x + 6x = ???

- anonymous

Were adding right? 12x^2

- jim_thompson5910

6 apples + 6 apples = ______ apples

- jim_thompson5910

the x doesn't become x^2 when you add 6x+6x

- anonymous

Oh, 6x+6x =12x

- jim_thompson5910

so we get x^2+12x+36

- jim_thompson5910

that's as far as we can go because there are no other like terms left to combine

- anonymous

Alright. Thanks @jim_thompson5910

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