Question

x^3+3x+3/x+1/x^3 factorize​

Answer 1

Answer:

$(x+\frac{1}{x} )^{3}$

Step-by-step explanation:

Given $x^{3}+3x+\frac{3}{x} + \frac{1}{x^{3} }$

This can be re-written as shown

$x^{3}+\frac{1}{x^{3} } +3x^{2} * (\frac{1}{x} ) + 3 *x* (\frac{1}{x})$

This is in the form of a³ + b³ +3a²b + 3ab² = (a + b)³

⇒ $x^{3}+\frac{1}{x^{3} } +3x^{2} * (\frac{1}{x} ) + 3 *x* (\frac{1}{x})$ = $(x+\frac{1}{x} )$³

Hope that helps you...☺

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Answer 2

Answer:

ʜᴇʀᴇ ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ :-

${x}^{3} + 3x + \frac{3}{x} + \frac{1}{ {x}^{3} } \\ = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times {x}^{2} \times \frac{1}{x} + 3 \times x \times \frac{1}{ {x}^{2} } \\ now \: \: in \: the \: above \: step \: we \: have \: split \: the \: question \: in \: the \: form \: of \\ {(a + b)}^{3} \\ since \\ {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2} b + 3 a{b}^{2} \\ so \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times {x}^{2} \times \frac{1}{x} + 3 \times x \times \frac{1}{ {x}^{2} } = {(x + \frac{1}{x}) }^{3}$

Hope it's helpful

Answered by :-

@MissInfinite