Simplify
$f (x) = {(2 x - 1)}^{2} + 3$

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Solution

We have,

$f (x) = {(2 x - 1)}^{2} + 3$

Now,

$f (x) = ({(2 x)}^{2} + 1^{2} - 2 \times 2 x \times 1) + 3$

$= (4 x^{2} + 1 - 4 x) + 3$

$= 4 x^{2} + 1 - 4 x + 3$

$= 4 x^{2} - 4 x + 4$

$= 4 (x^{2} - x + 1)$

Hence, this is the answer.

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