Question
Factorise:$4 a^2+\frac{1}{4 a^2}-2-6 a+\frac{3}{2 a}$
✓
Answer
$4 a^2+\frac{1}{4 a^2}-2-6 a+\frac{3}{2 a} $
$ =\left(4 a^2+\frac{1}{4 a^2}-2\right)-\left(6 a-\frac{3}{2 a}\right)$
$ =\left(2 a-\frac{1}{2 a}\right)^2-3\left(2 a-\frac{1}{2 a}\right) $
$ =\left(2 a-\frac{1}{2 a}\right)\left(2 a-\frac{1}{2 a}-3\right)$
$ =\left(4 a^2+\frac{1}{4 a^2}-2\right)-\left(6 a-\frac{3}{2 a}\right)$
$ =\left(2 a-\frac{1}{2 a}\right)^2-3\left(2 a-\frac{1}{2 a}\right) $
$ =\left(2 a-\frac{1}{2 a}\right)\left(2 a-\frac{1}{2 a}-3\right)$
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