Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5 - Page 75: 111

$(x-y)^{2}(x-y+2)(x-y-2)$

$(x-y)^{4}- 4(x-y)^{2}$ Takeout common factor $(x-y)^{2}$ $=(x-y)^{2}((x-y)^{2}-4)$ $=(x-y)^{2}((x-y)^{2}-2^{2})$ Use the formula $[(a^{2}-b^{2}) = (a+b)(a-b)]$ $=(x-y)^{2}((x-y)+2)((x-y)-2)$ $=(x-y)^{2}(x-y+2)(x-y-2)$