作业帮1.x2+(1+x)2+(x+x2)22.(x+y)4+(x2-y2)2+(x-y)4
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1.x2+(1+x)2+(x+x2)22.(x+y)4+(x2-y2)2+(x-y)4
1.x2+(1+x)2+(x+x2)2
2.(x+y)4+(x2-y2)2+(x-y)4
1.x2+(1+x)2+(x+x2)22.(x+y)4+(x2-y2)2+(x-y)4
x² + (1 + x)² + (x + x²)²
= (x² + x)² + (x² + 2x + 1) + x²
= (x² + x)² + 2(x² + x) + 1
= (x² + x + 1)²
(x+y)4+(x2-y2)2+(x-y)4
=(x+y)^4+(x+y)^2(x-y)^2+(x-y)^4
=(x+y)^4+2(x+y)^2(x-y)^2+(x-y)^4-(x+y)^2(x-y)^2
=[(x+y)^2+(x-y)^2]^2-(x^2-y^2)^2
=(2x^2+2y^2)^2-(x^2-y^2)^2
=[(2x^2+2y^2)+(x^2-y^2)][(2x^2+2y^2)-(x^2-y^2)]
=(3x^2+y^2)(x^2+3y^2)
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