Toán Lớp 8: b) x^3 + 6x^2y + 12xy^2 + 9y^3 c) 9x^3 + 12x^2y + 6xy^2 + y^3

Question

Toán Lớp 8:  b) x^3 + 6x^2y + 12xy^2 + 9y^3 c) 9x^3 + 12x^2y + 6xy^2 + y^3

quynhmaithu · Answer

Giải đáp+Lời giải và giải thích chi tiết:    b) x&sup3; + 6x&sup2;y + 12xy&sup2; + 9y&sup3;   = (x+2y)&sup3; + y&sup3;   = (x+2y+y)[(x+2y)&sup2; - y(x+2y) + y&sup2;]   = (3y+x)(x&sup2;+4xy+4y&sup2; - xy - 2y&sup2; + y&sup2;)   = (3y+x)(x&sup2; +3xy + 3y&sup2;)   c) 9x&sup3; + 12x&sup2;y + 6xy&sup2; + y&sup3;   = x&sup3; + 8x&sup3; + 12x&sup2;y + 6xy&sup2; + y&sup3;   = x&sup3; + (2x+y)&sup3;   = (x+2x+y)[x&sup2; - x(2x+y) + (2x+y)&sup2;]   = (3x+y)(x&sup2; - 2x&sup2; - xy + 4x&sup2; + 4xy + y&sup2;)   = (3x+y)(3x&sup2; + 3xy + y&sup2;)

tonhitruc · Answer

Giải đáp:   b) x^3 + 6x^2y + 12xy^2 + 9y^3   = x^3 + 6x^2y + 12xy^2 + 8y^3 + y^3   =x^3 + 3.x^2 . 2y + 3.x . (2y)^2 + (2y)^3 + y^3   = (x + 2y)^3 + y^3   =(x+ 3y ) ( x + 4xy + 4y^2 - xy - 2y^2 + y^2 )   = (x+ 3y)( x^2 + 3y^2 + 3xy)   c) 9x^3 + 12x^2y + 6xy^2 + y^3   = x^3 + 8x^3 + 12xy + 6xy^2 + y^3   = x^3 + ( 2x + y)^3   = (3x + y)( x^2 - 2x^2 - xy + 4x^2 - 4xy + y^2)   = (3x + y)(3x^2 - 5xy + y^2)