# How do you simplify (2x - 3) ^ { 2} + ( x - 5) ( x + 5) - ( x + 4)?

Apr 15, 2018

$= 5 {x}^{2} - 13 x - 20$

#### Explanation:

${\left(2 x - 3\right)}^{2} = \left(2 x - 3\right) \left(2 x - 3\right)$

$\implies$ $4 {x}^{2} - 6 x - 6 x + 9$

$\implies$ $4 {x}^{2} - 12 x + 9$

$\left(x - 5\right) \left(x + 5\right) = {x}^{2} + 5 x - 5 x - 25$

$\implies$ $= {x}^{2} - 25$

So if we put these altogether

$\left[4 {x}^{2} - 12 x + 9\right] + \left[{x}^{2} - 25\right] - \left(x + 4\right)$

$= 4 {x}^{2} - 12 x + 9 + {x}^{2} - 25 - x - 4$

$= 5 {x}^{2} - 13 x - 20$