Question 546994
Factor:
1. {{{216x^3-1}}} This is a difference of two cubes which can be factored thus:
{{{A^3-B^3 = (A-B)(A^2+AB+B^2)}}}
{{{216x^3-1 = (6x)^3-(1)^3}}}={{{highlight((6x-1)(36x^2+6x+1))}}}
2. {{{8x^3+125}}} This is a sum of two cubes which can be factored thus:
{{{A^3+B^3 = (A+B)(A^2-AB+B^2)}}}
{{{8x^3+125 = (2x)^3+(5)^3}}}={{{highlight((2x+5)(4x^2-10x+25))}}}
3. {{{x^4-5x^2+4}}} Temporarily change the varible: {{{x^2 = y}}}
{{{y^2-5y+4 = (y-1)(y-4)}}} Substitute {{{y = x^2}}}
{{{(x^2-1)(x^2-4) = highlight((x+1)(x-1)(x^2+4))}}}