SiMPle PrOBleM
Algebra
Level
pending
The total number of terms in the expansion of (X^2 + y^2)^60 + (x^2 – y^2)^60 , after simplification is :
31
30
29
60
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1 solution
( x 2 + y 2 ) 2 = ( x 2 + y 2 ) ( x 2 + y 2 ) = x 4 + 2 x 2 y 2 + y 4
( x 2 − y 2 ) 2 = ( x 2 − y 2 ) ( x 2 − y 2 ) = x 4 − 2 x 2 y 2 + y 4
x 4 + 2 x 2 y 2 + y 4 + x 4 − 2 x 2 y 2 + y 4 = 2 x 4 + 2 y 4 = 2 ( x 4 + y 4 )
So, in general:
( x a + y a ) n + ( x a − y a ) n = n where n is the exponent (i.e. the number of times you have to duplicate the brackets and the expression within the brackets.) and a , n are positive integers.
Applying this, the answer is 6 0 .