Toán Lớp 8: Phân tích nhân tử: a) (4x^2-4x+1)-(x+1) b) x^3+27 c) x^4+2x^2+1 d) x^3+1-x^2-x e) x^3-3x^2+3x-1 f) (x+y)^2-2(x+y)+1 g) x^4+y^4 h) x^2-

Question

Toán Lớp 8:  Phân tích nhân tử: a) (4x^2-4x+1)-(x+1) b) x^3+27 c) x^4+2x^2+1 d) x^3+1-x^2-x e) x^3-3x^2+3x-1 f)  (x+y)^2-2(x+y)+1 g) x^4+y^4 h) x^2-3y^2

buithaianh98 · Answer

Giải đáp:    a, (4x^2 - 4x + 1) - (x + 1)^2   = [(2x)^2 - 2.2x.1 + 1^2] - (x + 1)^2   = (2x - 1)^2 - (x + 1)^2   = [(2x - 1) - (x + 1)][(2x - 1) + (x + 1)]   = (2x - 1 - x - 1)(2x - 1 + x + 1)   = (x - 2).3x   b, x^3 + 27 = x^3 + 3^3   = (x + 3)(x^2 - x.3 + 3^2)   = (x + 3)(x^2 - 3x + 9)   c. x^4 + 2x^2 + 1   = (x^2)^2 + 2.x^2 . 1 + 1^2   = (x^2 + 1)^2   d, x^3 + 1 - x^2 - x   = (x^3 + 1) - (x^2 + x)   = (x + 1)(x^2 - x + 1) - x(x + 1)   = (x + 1)(x^2 - x + 1 - x)   = (x + 1)(x^2 - 2x + 1)   = (x + 1)(x - 1)^2   e, x^3 - 3x^2 + 3x - 1   = x^3 - 3.x^2 . 1 + 3.x.1^2 - 1^3   = (x - 1)^3   f, (x + y)^2 - 2(x + y) + 1   = (x + y)^2 - 2(x + y).1 + 1^2   = (x + y - 1)^2   g, x^4 + y^4   = x^4 + 2x^2 y^2 + y^4 - 2x^2 y^2   = (x^2)^2 + 2x^2 y^2 + (y^2)^2 - 2x^2 y^2   = (x^2 + y^2)^2 - ( sqrt{2xy})^2   = (x^2 + y^2 +  sqrt{2xy})(x^2 + y^2 -  sqrt{2xy})   h, x^2 - 3y^2   = x^2 - ( sqrt{3y})^2   = (x -  sqrt{3y})(x +  sqrt{3y})