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Question Number 192173 by universe last updated on 10/May/23

prove that (x^2 +a^2 )^4 = (x^4 −6x^2 a^2 +a^4 )^2 +(4x^3 a−4xa^3 )^2

provethat(x2+a2)4=(x4−6x2a2+a4)2+(4x3a−4xa3)2

Answered by mehdee42 last updated on 10/May/23

right side=((x^2 −a^2 )^2 −4a^2 x^2 )^2 +16a^2 x^2 (x^2 −a^2 )^2 (x^2 −a^2 )^4 −8a^2 x^2 (x^2 −a^2 )^2 +16a^2 x^2 +16a^2 x^2 (x^2 −a^2 )^2 (x^2 −a^2 )^4 +8a^2 x^2 (x^2 −a^2 )^2 +16a^2 x^2 ((x^2 −a^2 )^2 +4a^2 x^2 )^2 =(x^2 +a^2 )^2 ✓

rightside=((x2−a2)2−4a2x2)2+16a2x2(x2−a2)2(x2−a2)4−8a2x2(x2−a2)2+16a2x2+16a2x2(x2−a2)2(x2−a2)4+8a2x2(x2−a2)2+16a2x2((x2−a2)2+4a2x2)2=(x2+a2)2✓

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