Toán Lớp 8: rút gọn: a. (x-1)(x^2+x+1)-x(x-1)(x+1) b. (x-1)^3-(x+1)(x^2-x+1)+3x(x+2) mong mn giúp mik

Question

Toán Lớp 8:  rút gọn: a. (x-1)(x^2+x+1)-x(x-1)(x+1)                b. (x-1)^3-(x+1)(x^2-x+1)+3x(x+2) mong mn giúp mik

maitrucloan · Answer

Giải đáp:    a) x - 1   b) 9x - 2    Lời giải và giải thích chi tiết:    a)   (x - 1)(x^2 + x + 1) - x(x - 1)(x + 1)   = (x - 1)(x^2 + x.1 + 1^2) - x[(x - 1)(x + 1)]   = (x^3 - 1^3) - x(x^2 - 1^2)   = (x^3 - 1) - x(x^2 - 1)   = x^3 - 1 - x^3 + x   = (x^3 - x^3) + x - 1   = x - 1   * D&ugrave;ng HĐT 7: a^3 - b^3 = (a - b)(a^2 + ab + b^2)   * D&ugrave;ng HĐT 3: a^2 - b^2 = (a - b)(a + b)   b)   (x - 1)^3 - (x + 1)(x^2 - x + 1) + 3x(x + 2)   = (x^3 - 3.x^2 . 1 + 3.x.1^2 - 1^3) - (x + 1)(x^2 - x.1 + 1^2) + 3x^2 + 6x   = (x^3 - 3x^2 + 3x - 1) - (x^3 + 1^3) + 3x^2 + 6x   = x^3 - 3x^2 + 3x - 1 - x^3 - 1 + 3x^2 + 6x   = (x^3 - x^3) - (3x^2 - 3x^2) + (3x + 6x) - (1 + 1)   = 9x - 2   * D&ugrave;ng HĐT 5: (a - b)^3 = a^3 - 3a^2 b + 3ab^2 - b^3   * D&ugrave;ng HĐT 6: a^3 + b^3 = (a + b)(a^2 - ab + b^2)   #SunHee

tuyen98 · Answer

(x-1)(x^2+x+1)-x(x-1)(x+1)     = (x^3 - 1) - x(x^2 - 1)      = x^3 - 1 - x^3 + x     = x - 1     (x-1)^3-(x+1)(x^2-x+1)+3x(x+2)     = (x^3 - 3x^2 + 3x - 1) - (x^3 + 1) +(3x^2+6x)     = x^3 - 3x^2 + 3x - 1 - x^3 - 1 +3x^2+6x     = (x^3 - x^3) + (3x^2 - 3x^2) + (6x + 3x) - 1 -1     = 9x - 2