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A complete factorisation of x⁴ + 64 is?

1(x² + 8)²
2(x² + 8)(x² - 8)
3(x² - 4x + 8)(x² - 4x - 8)
4(x² + 4x + 8)(x² - 4x + 8)

Answer:- 1

Explanation:-

Solution:

\begin{aligned} (x^{4} + 64) \\ = x^{4} + 8^{2} + 2. x^{2} .8 - 2. x^{2} .8 \\ = {(x^{2} + 8)}^{2} - (16 x^{2}) \\ = {(x^{2} + 8)}^{2} - {(4 x)}^{2} \\ = (x^{2} + 8 + 4 x) (x^{2} + 8 - 4 x) \\ = (x^{2} + 4 x + 8) (x^{2} - 4 x + 8) \end{aligned}

$\eqalign{ & \left( {{x^4} + 64} \right) \cr & = {x^4} + {8^2} + 2.{x^2}.8 - 2.{x^2}.8 \cr & = {\left( {{x^2} + 8} \right)^2} - \left( {16{x^2}} \right) \cr & = {\left( {{x^2} + 8} \right)^2} - {\left( {4x} \right)^2} \cr & = \left( {{x^2} + 8 + 4x} \right)\left( {{x^2} + 8 - 4x} \right) \cr & = \left( {{x^2} + 4x + 8} \right)\left( {{x^2} - 4x + 8} \right) \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} (x^{4} + 64) \\ = x^{4} + 8^{2} + 2. x^{2} .8 - 2. x^{2} .8 \\ = {(x^{2} + 8)}^{2} - (16 x^{2}) \\ = {(x^{2} + 8)}^{2} - {(4 x)}^{2} \\ = (x^{2} + 8 + 4 x) (x^{2} + 8 - 4 x) \\ = (x^{2} + 4 x + 8) (x^{2} - 4 x + 8) \end{aligned}

$\eqalign{ & \left( {{x^4} + 64} \right) \cr & = {x^4} + {8^2} + 2.{x^2}.8 - 2.{x^2}.8 \cr & = {\left( {{x^2} + 8} \right)^2} - \left( {16{x^2}} \right) \cr & = {\left( {{x^2} + 8} \right)^2} - {\left( {4x} \right)^2} \cr & = \left( {{x^2} + 8 + 4x} \right)\left( {{x^2} + 8 - 4x} \right) \cr & = \left( {{x^2} + 4x + 8} \right)\left( {{x^2} - 4x + 8} \right) \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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