Đáp án + Giải thích các bước giải:
\(1)\\x^2-y^2-2x+2y\\=(x-y)(x+y)-2(x-y)\\=(x-y)(x+y-2)\\2)\\2x+2y-x^2-xy\\=2(x+y)-x(x+y)\\=(2-x)(x+y)\\3)\\3a^2-6ab+3b^2-12c^2\\=3(a^2-2ab+b^2-4c^2)\\=3[(a-b)^2-(2c)^2]\\=3(a-b-2c)(a-b+2c) \\4)\\a^2+2ab+b^2-c^2\\=(a+b)^2-c^2\\=(a+b-c)(a+b+c)\\5)\\x^2-25+y^2+2xy\\=(x^2+2xy+y^2)-25\\=(x+y)^2-5^2\\=(x+y-5)(x+y+5)\\6)\\x^2-2x-4y^2-4y\\=(x^2-4y^2)-(2x+4y)\\=(x-2y)(x+2y)-2(x+2y)\\=(x+2y)(x-2y-2)\\7)\\x^2(x-1)+16(1-x)\\=x^2(x-1)-16(x-1)\\=(x^2-16)(x-1)\\=(x-4)(x+4)(x-1)\\8)\\x^2-xy+x-y\\=x(x-y)+(x-y)\\=(x+1)(x-y)\\9)\\3(x+4)-x^2-4x\\=3x+12-x^2-4x\\=-x^2-x+12\\=-(x^2+x-12)\\=-(x^2+4x-3x-12)\\=-[x(x+4)-3(x+4)]\\=-(x-3)(x+4)\\10)\\x^3+x^2y-4x-4y\\=x^2(x+y)-4(x+y)\\=(x^2-4)(x+y)\\=(x-2)(x+2)(x+y)\\11)\\2x^2+3x-5\\=2x^2-2x+5x-5\\=2x(x-1)+5(x-1)\\=(2x+5)(x-1)\\12)\\x^2-2x-15\\=(x^2-2x+1)-16\\=(x-1)^2-4^2\\=(x-1-4)(x-1+4)\\=(x-5)(x+3)\\13)\\x^2+8x+7\\=x^2+7x+x+7\\=x(x+7)+(x+7)\\=(x+1)(x+7)\\14)\\x^4+6x^2y+9y^2-1\\=(x^4+6x^2y+9y^2)-1\\=(x^2+3y)^2-1\\=(x^2+3y-1)(x^2+3y+1)\\15)\\2x^2-18\\=2(x^2-9)\\=2(x-3)(x+3)\)
