Question

(2a^x + b^x)^2

Answer 1

Remember, an exponent to an exponent is simply multiplying the two exponents together... so (2a^x + b^x)^2 becomes

2a^(x*2) + b^(x*2)

Does that makes sense?

Answer 2

so then it would be 2a*2x+b*2x?

Answer 3

No, don't lose the exponent markers:

It would actually be 2a^2x + b^2x

Answer 4

Does that make sense?

Answer 5

yes, so then i'd have to evaluate the exponents right?

Answer 6

Yes, but in this case, you'll have to just leave them alone because in both bases you have a variable, so you can't do anything further.

Answer 7

oh my gosh i forgot to add the 1/2 in front of the b :((((((

Answer 8

That's okay, it doesn't make a difference, because it's still attached to the b, a variable:

2a^2x + 0.5b^2x

yes?

Answer 9

Ok, that makes sense. So if there is a variable in the base I'm done?

Answer 10

Pretty much!! :)

Answer 11

ok, cool thank you!

Answer 12

No prob!

Answer 13

Be careful!
Example:
\[\large (ax + bx)^2 \cancel{=} ax^2 + bx^2\]
\[\large (ax + bx)^2 = (ax + bx)(ax + bx)\]

Answer 14

@woodsymte Another term is missing in-between as johnweldon said.

Answer 15

ok so then in that case would it be \[ (2a ^{x}+b ^{x})+(2a ^{x}+b ^{x})\]

Answer 16

@sachintha

Answer 17

There is no plus sign in the middle *Use what I have written above as a reference*

\[\large (2a^x + b^x)(2a^x + b^x) = ?\]

Now just expand it out, foil method or whatever it is called now-a-days haha

Answer 18

so \[4a ^{2x}+4a ^{2x}b ^{2x}+2b ^{2x}\]

Answer 19

@johnweldon1993

Answer 20

The first term is correct, check the second and third terms though

Just write out the foil method

\[\large 2a^x \times 2a^x\]
\[\large 2a^x \times b^x\]
\[\large b^x \times 2a^x\]
\[\large b^x \times b^x\]

Answer each f those...then add them all

Answer 21

Ok so I did it again but I'm still getting the same answer so I don't see where I'm going wrong. When I multiply the 2a^x and b^x I get 2a^xb^x right?

Answer 22

I'm having trouble don't be rude

Answer 23

@AloneS

Answer 24

yes
\[2a^x \cdot b^x \text{ is } 2a^{x} b^{x} \text{ or you can write it as } 2 (ab)^x \\ \text{ if preferred }\]

Answer 25

So when I combine them they would be4a^2xb^2x?

Answer 26

assume you are talking about with another term in the expansion of your multiplication
you know where you have
\[b^x \cdot 2a^{x} \text{ which is also } 2a^{x}b^{x} \text{ or } 2 (ab)^x \\ \text{ and yes } \\ 2(ab)^{x}+2(ab)^{x} \text{ is } 4(ab)^{x}\]

Answer 27

since 2+2 is 4
or since 2 apples + another 2 apples is 4 apples
basically we can combine those terms since they are like terms (they have the same variable part)

Answer 28

So why did he tell me it was wrong?

Answer 29

because you had 4a^(2x)b^(2x)

Answer 30

your last term was also incorrect

Answer 31

Oh ok so I just had to put them in parenthesis?

Answer 32

\[4a ^{2x}+4a ^{2x}b ^{2x}+2b ^{2x}\]
assume you were talking about this right?
this was your answer?

Answer 33

Yes it was

Answer 34

Like I said I'm sorry but this isn't the appropriate setting in which to handle that. Obviously she is less than agreeable but I'm trying to get help.

Answer 35

you guys please delete your conversation
this is a serious question for math help


and this was the problem
\[(2a^x+b^x)^2\]

Answer 36

Wait what do you mean that was what I did?

Answer 37

I'm really sorry I think I'm just overthinking it but math is a foreign language to me

Answer 38

\[(2a^x+b^x)^2=(2a^{x}+b^{x})(2a^x+b^{x}) \\ \]
take first term from first ( ) and multiply it to everything in second ( )
then
plus
then
take second term from first ( ) and multiply it to everything in second ( )

\[2a^x(2a^x+b^x)+b^{x}(2a^{x}+b^{x}) \\ 2a^{x}(2a^{x})+2a^{x}(b^{x})+b^{x}(2a^{x})+ b^{x}(b^{x})\]

Answer 39

so you already did those two middle terms and found out they were like terms

Answer 40

right

Answer 41

\[2a^{x}(2a^{x})+4a^{x}b^{x}+b^{x}(b^{x})\]

based on your earlier answer you did the first term correctly since 2*2 is 4
and a^(x) times a^(x) is a^(x+x) or a^(2x)


but your last term still needs work
\[4a^{2x}+4a^{x}b^{x}+b^{x}(b^{x})\]

Answer 42

It'd be \[2b ^{2x}\]?

Answer 43

no where are you getting the 2 in front ?

Answer 44

because I'm... ohhhhh I'm adding those and I should be multiplying

Answer 45

so then it's just \[b ^{2x}\]

Answer 46

right

Answer 47

if you had b^(x) + b^(x) you would say 2b^(x)
but you have b^(x)*b^(x) which is b^(2x)

and if you ahd 2b^(x)*b^(x) then you could say 2b^(2x)

Answer 48

oh my gosh that was ridiculous. Thank you sooooooo much

Answer 49

np