How do you factor (x-1)^2 - 4?

May 12, 2018

$\left(x - 3\right) \left(x + 1\right)$

$\left\{3 , - 1\right\}$

Explanation:

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

Factor out:

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

Factor:

$\left(x - 3\right) \left(x + 1\right)$

$\left\{3 , - 1\right\}$

May 12, 2018

$\left(x + 1\right) \left(x - 3\right)$

Explanation:

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

To factorise the expression we could first expand the first term. However, in this case, notice that the expression is the difference of two squares.

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

Remember the common identity: ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

Thus, Expression $= \left(x - 1 + 2\right) \left(x - 1 - 2\right)$

$= \left(x + 1\right) \left(x - 3\right)$