$1)5x^2-5y^2-10x+10y\\=5(x-y)(x+y)-10(x-y)\\=(x-y)(5x+5y-10)\\=5(x-y)(x+y-2)\\2)x^2-2x-4y^2+4y^2\\=x^2-2x\\=x(x-2)\\3)x^2-25+y^2+2xy\\=(x+y)^2-25\\=(x+y-5)(x+y+5)\\4)x^2-y^2+4x+4\\=(x+2)^2-y^2\\=(x-y+2)(x+y+2)\\5)x^3+x^2y-4x-4y\\=x^2(x+y)-4(x+y)\\=(x+y)(x-2)(x+2)\\=6)x^4+6x^2y+9y^2-1\\=(x^2+3y)^2-1\\=(x^2+3y-1)(x^2+3y+1)\\7)2xy^2-x^2y-y^3\\=-y(x^2-2xy+y^2)\\=-y(x-y)^2\\9)3x^2-6xy+3y^2-12z^2\\=3[(x-y)^2-4z^2]\\=3(x-y-2z)(x-y+2z)\\9)a^4-4a^3+4a^2\\=(a^2-2a)^2\\=[a(a-2)]^2\\=a^2(a-2)^2\\10)a^2-2a-b^2+2b\\=(a-b)(a+b)-2(a-b)\\=(a-b)(a+b-2)$
