Verified answer

Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\sf \dfrac{a^4 - b^4}{a^2 + 2ab + b^2}\:.\:\dfrac{a^2 - b^2}{a^2 + b^2}[/tex]

[tex]\sf \dfrac{a^4 - b^4}{(a + b)\:\:(a + b)}\:.\:\dfrac{a^2 - b^2}{a^2 + b^2}[/tex]

[tex]\sf \dfrac{a^4 - b^4}{(a + b)\:.\:(a + b)}\:.\:\dfrac{(a + b)\:.\:(a - b)}{a^2 + b^2}[/tex]

[tex]\sf \dfrac{(a^2 + b^2)\:.\:(a + b)\:.\:(a - b)}{(a + b)}\:.\:\dfrac{(a - b)}{a^2 + b^2}[/tex]

[tex]\sf (a - b)\:.\:(a - b)[/tex]

[tex]\sf \dfrac{a^4 - b^4}{a^2 + 2ab + b^2}\:.\:\dfrac{a^2 - b^2}{a^2 + b^2} = (a - b)^2[/tex]

[tex]\sf a - b = 3[/tex]

[tex]\boxed{\boxed{\sf \dfrac{a^4 - b^4}{a^2 + 2ab + b^2}\:.\:\dfrac{a^2 - b^2}{a^2 + b^2} = 9}}[/tex]