L.H.S=(a+b)4-(a-b)4Suppose, a+b=x and a-b=y∴(a+b)4-(a-b)4=x4-y4=(x2)2-(y2)2=((x2+y2)(x2-y2)=(x2+y2)(x+y)(x-y)=[(a+b)2+(a-b)2][(a+b+a-b)(a+b-a+b) =[(a+b)2+(a-b)2](2a×2b)=4ab[(a+b)2+(a-b)2]=4ab(a2+2ab+b2+a2-2ab+b2)=4ab(2a2+2b2)=4ab×2(a2+b2)=8ab(a2+b2)R.H.S (PROVED)
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