Question
Solve:
$ (2 x+1)^2-9 x^4 $
$ (2 x+1)^2-9 x^4 $
✓
Answer
$ (2 x+1)^2-9 x^4 $
$= (2 x+1)^2-\left(3 x^2\right)^2 $
$= {\left[(2 x+1)-3 x^2\right]\left[(2 x+1)+3 x^2\right] } $
$= \left(-3 x^2+2 x+1\right)\left(3 x^2+2 x+1\right) $
$= \left(-3 x^2+3 x-x+1\right)\left(3 x^2+2 x+1\right) $
$= \{3 x(x-1)+1(-x+1)\}\left(3 x^2+1\right) $
$= (-x+1)(3 x+1)\left(3 x^2+2 x+1\right) $
$= -(x-1)(3 x+1)\left(3 x^2+2 x+1\right) $
$= (2 x+1)^2-\left(3 x^2\right)^2 $
$= {\left[(2 x+1)-3 x^2\right]\left[(2 x+1)+3 x^2\right] } $
$= \left(-3 x^2+2 x+1\right)\left(3 x^2+2 x+1\right) $
$= \left(-3 x^2+3 x-x+1\right)\left(3 x^2+2 x+1\right) $
$= \{3 x(x-1)+1(-x+1)\}\left(3 x^2+1\right) $
$= (-x+1)(3 x+1)\left(3 x^2+2 x+1\right) $
$= -(x-1)(3 x+1)\left(3 x^2+2 x+1\right) $
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