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

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Answer 1 · 2018-05-12T01:21:47

$(x-3)(x+1)$

${3,-1}$

$(x-1)^2-4$

Factor out:

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

Factor:

$(x-3)(x+1)$

${3,-1}$

Answer 2 · 2018-05-12T01:25:24

$(x+1)(x-3)$

Expression $= (x-1)^2-4$

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 $= (x-1)^2 - 2^2$

Remember the common identity: $a^2 - b^2 = (a+b)(a-b)$

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

$= (x+1)(x-3)$

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