WHICH OF THE FOLLOWING EXPRESSIONS DES NOT BELONG TO A GROUP
A. ¼x⁴-1
B. X²-0.0001y⁴
C. 8(X-1)³-27
D. (X+1)⁴ -4x⁴
Answers
Given : Different expressions
To Find : Which one is odd one out
A. ¼x⁴-1
B. x²-0.0001y⁴
C. 8(x-1)³-27
D. (x+1)⁴ -4x⁴
Solution:
A. ¼x⁴-1
= (x²/2)² - 1²
a² - b²
B. x²-0.0001y⁴
= x²- (0.01y²)²
a² - b²
C. 8(x-1)³-27
= (2(x - 1))³ - 3³
a³ - b³
D. (x+1)⁴ -4x⁴
= ((x+1)²)² - (2x²)²
a² - b²
Hence C. 8(x-1)³-27 is different as all others are of form a² - b² while it is of form a³ - b³
Another logic , degrees of ¼x⁴-1 , x²-0.0001y⁴ and (x+1)⁴ -4x⁴ is 4
and degree of 8(x-1)³-27 is 3
Hence C. 8(x-1)³-27 does not belong to a group
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