Simplifique isto de modo a cortar o h do denominador. [(2 + h)^4 - 16]/h.... Pergunta de ideia deEggdoido

Eggdoido @Eggdoido

December 2019 1 136 Report

Simplifique isto de modo a cortar o h do denominador.

[(2 + h)^4 - 16]/h

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GFerraz Olá.

Produto notável utilizado:

a² - b² = (a-b)(a+b)

Assim:

(2+h)⁴ - 16 = [(2+h)² - 4][(2+h)² + 4]
= (4 + 4h + h² - 4)(4 + 4h + h² + 4)
= (4h + h²)(h² + 4h + 8)
= h(4 + h)(h² + 4h + 8)

Então, podemos dizer que:

$\dfrac{(2+h)^4 - 16}{h} = \dfrac{h(4+h)(h^2+4h+8)}{h} = \boxed{(4+h)(h^2+4h+8)}$

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