## anonymous one year ago (x+6)^2 Is this right? (x+6)^2 =36x

1. LynFran

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

2. anonymous

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

3. SolomonZelman

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

4. anonymous

Nope.

5. 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?

6. anonymous

? What is expression 1 and 2 suppose to mean?

7. SolomonZelman

any expreesions, i am just naming them like this.

8. SolomonZelman

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

9. anonymous

Okay.

10. SolomonZelman

good.

11. 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.

12. SolomonZelman

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

13. SolomonZelman

a(b) = a•b = ab

14. SolomonZelman

all 3 parts are same...

15. anonymous

Alright

16. 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

17. SolomonZelman

I am multiplying everything inside the parenthesis times a.

18. SolomonZelman

is this making some sense?

19. anonymous

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

20. anonymous

@SolomonZelman

21. anonymous

Anyone?

22. jdoe0001

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

23. anonymous

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

24. 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|

25. jim_thompson5910

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

26. anonymous

yeah.

27. 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|

28. 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.

29. jim_thompson5910

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

30. anonymous

Okay.

31. anonymous

Sooo?

32. jim_thompson5910

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

33. anonymous

48x^2

34. jim_thompson5910

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

35. jim_thompson5910

6x and 36 aren't like terms

36. anonymous

12x^2

37. jim_thompson5910

6x + 6x = ???

38. anonymous

39. jim_thompson5910

6 apples + 6 apples = ______ apples

40. jim_thompson5910

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

41. anonymous

Oh, 6x+6x =12x

42. jim_thompson5910

so we get x^2+12x+36

43. jim_thompson5910

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

44. anonymous

Alright. Thanks @jim_thompson5910