Solve: (2 x+1)^2-9 x^4 - Vidyadip

Question

Solve:
$(2 x+1)^2-9 x^4$

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Answer

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

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