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The expression $x^{2} - y^{2} - 4 x + 4$ factorises as:

Competition practiceAlgebra

A $(x + y - 2) (x - y + 2)$
B $(x - y + 2) (x + y + 2)$
C $(x + y - 2)^{2}$
D $(x - 2 - y) (x - 2 + y)$

Step-by-Step Solution

Group the perfect square first:

x^{2} - 4 x + 4 - y^{2} = (x - 2)^{2} - y^{2}

. As a difference of squares this is

(x - 2 - y) (x - 2 + y)

.

Answer: D)

(x - 2 - y) (x - 2 + y)

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