Let's expand the expression: ( y 2 + 2 y ) 2 (y 2 +2y) 2 This is a perfect square, so we can use the identity: ( + ) 2 = 2 + 2 + 2 (a+b) 2 =a 2 +2ab+b 2 Let: = y 2 a=y 2 = 2 y b=2y Then: ( y 2 + 2 y ) 2 = ( y 2 ) 2 + 2 ( y 2 ) ( 2 y ) + ( 2 y ) 2 (y 2 +2y) 2 =(y 2 ) 2 +2(y 2 )(2y)+(2y) 2 Now compute each term: ( y 2 ) 2 = y 4 (y 2 ) 2 =y 4 2 ( y 2 ) ( 2 y ) = 4 y 3 2(y 2 )(2y)=4y 3 ( 2 y ) 2 = 4 y 2 (2y) 2 =4y 2 So the result is: y 4 + 4 y 3 + 4 y 2 y 4 +4y 3 +4y 2
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