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

2 Answers
May 12, 2018

Answer:

#(x-3)(x+1)#

#{3,-1}#

Explanation:

#(x-1)^2-4#

Factor out:

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

Factor:

#(x-3)(x+1)#

#{3,-1}#

May 12, 2018

Answer:

#(x+1)(x-3)#

Explanation:

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)#