` x^4 - x^2 + 2x - 1 `
` = (x^2)^2 - (x^2 - 2x + 1) `
` = (x^2)^2 - (x - 1)^2 `
` = (x^2 - x + 1)(x^2 + x - 1) `
` x^4 - 4x^3 - 8x^2 + 8x `
` = x(x^3 + 8 - 4x^2 - 8x) `
` = x[(x + 2)(x^2 - 2x + 4) - 4x(x + 2)] `
` = x(x + 2)(x^2 - 2x + 4 - 4x) `
` = x(x + 2)(x^2 - 6x + 4) `
` x^3 - 4x^2 + 4x - 1 `
` = (x^3 - 1) - (4x^2 - 4x) `
` = (x - 1)(x^2 + x + 1) - 4x(x - 1) `
` = (x - 1)(x^2 + x + 1 - 4x) `
` = (x - 1)(x^2 - 3x + 1) `
` x^3 + x^2 y - xy^2 - y^3 `
` = x^2 (x + y) - y^2 (x + y) `
` = (x + y)(x^2 - y^2) `
` = (x + y)(x - y)(x + y) `
` = (x + y)^2 (x - y) `
` x^2 y^2 + 1 - x^2 - y^2 `
` = (x^2 y^2 - x^2) + (1 - y^2) `
` = x^2(y^2 - 1) - (y^2 - 1) `
` = (y^2 - 1)(x^2 - 1) `
` = (y - 1)(y + 1)(x - 1)(x + 1) `
` x^3 - y^3 + 3y - 3x `
` = (x - y)(x^2 + xy + y^2) - 3(x - y) `
` = (x - y)(x^2 + xy + y^2 - 3) `
