# What is the standard form of f(x)=(x-1)^2-(2x-1)^2 ?

Feb 20, 2016

$- 3 {x}^{2} + 2 x$

#### Explanation:

distribute both 'pairs' of brackets using FOIL ( or by any method you may use).

${\left(x - 1\right)}^{2} = {x}^{2} - 2 x + 1$

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

Put these expansions back into 'original' expression.

$\Rightarrow {x}^{2} - 2 x + 1 - \left(4 {x}^{2} - 4 x + 1\right)$

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