(2m+n)(6m+2n)-(m-3n)(8m+16n) = 12m^2 + 4mn + 6m*2n + 2n^2 - 8m^2 - 16mn + 3mn - 48n^2 = 4m^2 - 8mn - 46n^2m^2 - mn + am - an = m(m - n) + a(m - n) = (m + a)(m - n)a^3 + 5a^2 + 5a + 25 = a^2(a + 5) + 5(a + 5) = (a^2 + 5)(a + 5)b^3 + b^2c - b^2d - bcd = b(b^2 + bc - bd - cd)x^2 + x - y^2 - y = (x + y)(x - y + 1)a^3 + a + b^3 + b = a(a^2 + 1) + b(b^2 + 1) = (a + b)(a^2 + b^2 + 1)x^16 - y^16 = (x^8 + y^8)(x^8 - y^8) = (x^8 + y^8)(x^4 + y^4)(x^4 - y^4) = (x^8 + y^8)(x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = (x^8 + y^8)(x^4 + y^4)(x^2 + y^2)(x + y)(x - y)x^2 - 5x - 14 = (x + 2)(x - 7)y^2 - 4y - 12 = (y - 6)(y + 2)a^4 + a^2 - 2 = (a^2 + 2)(a^2 - 1) = (a^2 + 2)(a + 1)(a - 1)b^4 + b^2 + 1 = (b^2 + b + 1)(b^2 - b + 1)x^4 - 8x^2 + 4 = (x^2 - 4)(x^2 - 1) = (x + 2)(x - 2)(x + 1)(x - 1)x^8 + 3x^4 + 4 = (x^4 + 1)(x^4 + 4) = (x^4 + 1)(x^2 + 2)(x^2 - 2)x^3 - 3x^2 + 3x + 7 = x^2(x - 3) + 3(x - 3) = (x^2 + 3)(x - 3)