Toán Lớp 8: phân tích đa thức thanh nhân tử a,4x^4-32x^2+1 b,x^2-2x-4y^2-4y c,x^4-2x^3+2x-1 d,x^4+2x^3-4x-4

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Toán Lớp 8:  phân tích đa thức thanh nhân tử  a,4x^4-32x^2+1 b,x^2-2x-4y^2-4y c,x^4-2x^3+2x-1 d,x^4+2x^3-4x-4

huenthanh97 · Answer

Giải đáp+Lời giải và giải thích chi tiết:    a) 4x^4 - 32x&sup2; + 1   = 4x^4 + 4x&sup2; + 1 - 36x&sup2;   = (2x&sup2; + 1)&sup2; - (6x)&sup2;    = (2x&sup2; + 1 - 6x)(2x&sup2; + 1 + 6x )   b) x&sup2; - 2x - 4y&sup2; - 4y   = (x&sup2; - 4y&sup2;) - (2x + 4y)   = (x-2y)(x+2y) - 2(x+2y)   = (x+2y)(x-2y -2)   c) x^4 - 2x&sup3; + 2x -1   = x^4 - 3x&sup3; + 3x&sup2; - x + x&sup3; - 3x&sup2; + 3x - 1   = (x^4 - 3x&sup3; + 3x&sup2; - x) + (x&sup3; - 3x&sup2; + 3x - 1)   = x(x&sup3; - 3x&sup2; + 3x - 1) + (x&sup3; - 3x&sup2; + 3x - 1)   = x(x-1)&sup3; + (x-1)&sup3;   = (x+1)(x-1)&sup3;   d) x^4 + 2x&sup3; - 4x - 4   = x^4 + 2x&sup3; + 2x&sup2; - 2x&sup2; - 4x - 4   = (x^4 + 2x&sup3; + 2x&sup2;) - (2x&sup2; + 4x + 4)   = x&sup2;(x&sup2; + 2x + 2) - 2(x&sup2; + 2x + 2)   = (x&sup2; + 2x + 2)(x&sup2; - 2)

dongoclandiem · Answer

Giải đáp:   a, 4x^4 - 32x^2 + 1   = 4x^4 - 12x^3 + 12x^2 + 2x^2 - 36x^2 + 2x^2 + 6x - 6x + 1   = 2x^2(2x^2-6x+1)+6x(2x^2-6x+1)+2x^2-6x+1   = (2x^2-6x+1)(2x^2+6x+1)   b, x^2 - 2x - 4y^2 + 4y   = x^2 - 4y^2 - 2x + 4y   = (x-2y)(x+2y)-2(x-2y)   = (x-2y)(x+2y-2)   c, x^4 - 2x^3 + 2x - 1   = (x^2-1)(x^2+1)-2x(x^2-1)   = (x-1)(x+1)(x^2+1)-2x(x-1)(x+1)   = (x-1)(x+1)(x^2-2x+1)   = (x-1)^3(x+1)   d, x^4 + 2x^3-4x-4   = (x^2)^2 - 2^2 + 2x^3 - 4x   = (x^2-2)(x^2+2)+2x(x^2-2)   = (x^2-2)(x^2+2+2x)