Question

ajuda rápido!!! preciso para hoje!

Answer 1

x^6+x^4+x²*y²+y^4-y^6

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(x²-y²)³ =x^6-3x^4y²+3x²y^4-y^6

(x²-y²)³ =x^6-y^6-3x²y²(x²-y²)

x^6-y^6=(x²-y²)³+3x²y²(x²-y²)

x^6-y^6=(x²-y²)[(x²-y²)²+3x²y²]

x^6-y^6=(x²-y²)[x^4+y^4-2x²y²+3x²y²]

x^6-y^6=(x²-y²)(x^4+y^4+x²y²)   (i)

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x^6+x^4+x²*y²+y^4-y^6

Arrumando convenientemente

x^6-y^6 +x^4+y^4+x²*y²  (ii)

inserindo (i)  em (ii)

(x²-y²)(x^4+y^4+x²y²)+(x^4+y^4+x²*y²)

(x^4+y^4+x²*y²)(x²-y²+ 1)  (iv)

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(a-b+c)*(a+b+c) =a²+ab+ac-ab-b²-bc+ac+bc+c²

(a-b+c)*(a+b+c) =a²-b²+2ac+c²

a²+c²=(a-b+c)*(a+b+c) -2ac +b²

fazendo a=x² ,  b=xy  e c=y²

x^4+y^4=(x²-xy+y²)*(x²+xy+y²) -2x²y² +x²y² 

x^4+y^4=(x²-xy+y²)*(x²+xy+y²) -x²y²  (v)


Inserindo (v)  em (iv)


((x²-xy+y²)*(x²+xy+y²) -x²y²+x²*y²)(x²-y²+ 1)


=(x²-xy+y²)*(x²+xy+y²)*(x²-y²+ 1)  é a resposta