Giải toán 8 tập 1: Câu 79 sgk trang 33

a) \(x^2 - 4 + (x - 2)^2\)
\(= (x^2- 2^2) + (x - 2)^2\)
\(= (x - 2)(x + 2) + (x - 2)^2\)
\(= (x - 2)[(x + 2) + (x -2)]\)
\(= (x - 2)(x + 2 + x - 2)\)
\(= (x - 2)(2x) \)
\(= 2x(x - 2)\)
b) \(x^3 - 2x^2 + x - xy^2\)
\(= x(x^2 - 2x + 1 - y^2)\)
\(= x[(x - 1)^2 - y^2]\)
\(= x(x - 1 + y)(x - 1 - y)\)
c) \(x^3 - 4x^2 - 12x + 27\)
\(= (x^3 + 27) - (4x^2 + 12x)\)
\(= (x^3 + 3^3) - 4x(x + 3)\)
\(= (x + 3)(x^2 - 3x + 9) - 4x(x + 3)\)
\(= (x + 3)(x^2 - 3x + 9 - 4x)\)
\(= (x + 3)(x^2 - 7x + 9)\)