to the 4th power!!

(x+3)^4 + (x-3)^4 =

(x+3)^4 =((x+3)^2)^2)
= (x^2 +6x + 9) ^2
=x^4 +12x^3 +54x^2 +108x +81

(x-3)^4 = ((x-3)^2)^2
= (x^2 -6x +9)^2
=x^4 -12x^3 +54x^2 -108x +81


answer = 2x^4 +108x^2 +162
 
(x+3)^4 + (x-3)^4

= [(x + 3)^2 + (x - 3)^2]^2 - 2(x + 3)^2(x - 3)^2
(same way as a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2)

= (2x^2 + 18)^2 - 2(x^4 - 18x^2 + 81)

= 4x^4 + 72x^2 + 324 - 2x^4 + 36x^2 - 162

= 2x^4 + 108x^2 + 162

= 2(x^4 + 54x^2 + 81) = same as apm!
 
thank for ur replies!!

but can someone explain how they did that. like when u do
(a + b)^2 u use FOIL,

but is it the same method for
(a + b)^n , where n is any number greater than 2
 
yes, you multiply it out

(a + b)^3 = (a + b)(a + b)(a + b) so you can start out by doing (a + b)^2 and then multiply the resulting answer by (a + b)

EX. (a + b)^3 = (a^2 +2ab + b^2)(a + b)

For greater powers, I recommend using pascals triangle.
 
HELP!!!!

What does ^ mean??
In questions I have received, they had problems like, (x+13)^4 and I had no clue what ^ meant, so I could not help them. Please tell me.
 
The carat symbol is used to indicate exponentiation.

Eliz.
 
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