Question

Factorise the following :x^3+1/x^3+6x+6/x.​

Answer 1

Answer:

$\displaystyle{ }\ \ \ \ x^3+\frac1{x^3}+6x+\frac6x\\\\=x^3 + 3x+\frac3x+\frac1{x^3}+3x+\frac3x\\\\=\left(x^3 + 3(x^2)(\tfrac1x)+3(x)(\tfrac1x)^2+(\tfrac1x)^3\right) + 3\left(x+\tfrac1x\right)\\\\=\left(x+\tfrac1x\right)^3 + 3\left(x+\tfrac1x\right)\\\\=\left(x+\tfrac1x\right)\left(\left(x+\tfrac1x\right)^2+3\right)\\\\=\left(x+\tfrac1x\right)\left(x^2+5+\tfrac1{x^2}\right)$

Answer 2

Answer:

(x+1/x)(x²+1/x²+5)

Step-by-step explanation:

• x³+1/x³+6x+6/x=
• (x+1/x)(x²-x*1/x+1/x²) + 6(x+1/x)=
• (x+1/x)(x²-1+1/x²+6)=
• (x+1/x)(x²+1/x²+5)