Maths

Example:

$(x+y+3)_{2}$

$=x_{2}+y_{2}+9+2xy+6y+6x$

$(a+b)_{3}=a_{3}+b_{3}+3a_{2}b+3ab_{2}$

$(a−b)_{3}=a_{3}−b_{3}−3a_{2}b+3ab_{2}$

Example:

$(x+3)_{3}$

$=x_{3}+27+9x_{2}+27x$

Factorise: $27x_{3}+1$

Here, $1$ can be regarded as having been raised to any power we like, so $(3x)_{3}+1_{3}$

$27x_{3}+1=(3x)_{3}+1_{3}$

$=(3x+1)((3x)_{2}−(3x)(1)+1_{2})$

$=(3x+1)(9x_{2}−3x+1)$

This is $x_{3}−2_{3}$, so we get:

*$x_{3}−2_{3}=x_{3}−2_{3}$*

* = $(x−2)(x_{2}+2x+2_{2})$*

* = $(x−2)(x_{2}+2x+4)$*

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