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Question
Factorize each of the following expression:
(2x + 1)2 − 9x4
Solution
\[(2x + 1 )^2 - 9 x^4 \]
\[ = (2x + 1 )^2 - (3 x^2 )^2 \]
\[ = [(2x + 1) - 3 x^2 ][(2x + 1) + 3 x^2 ]\]
\[ = ( - 3 x^2 + 2x + 1)(3 x^2 + 2x + 1)\]
We can factorise the quadratic expressions in the curved brackets as:
\[( - 3 x^2 + 3x - x + 1)(3 x^2 + 2x + 1)\]
\[ = \left\{ 3x( - x + 1) + 1( - x + 1) \right\}(3 x^2 + 2x + 1)\]
\[ = ( - x + 1)(3x + 1)(3 x^2 + 2x + 1)\]
\[ = - (x - 1)(3x + 1)(3 x^2 + 2x + 1)\]
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