Toán Lớp 8: b,(x+y)^2=x^2+2xy+y^2 c,(x-y)^2=x^2-2xy+y^2 d,(x+y)(x^3-xy+y^2)=x^3+y^3 e,(x-y)(x^3

Question

Toán Lớp 8:  b,(x+y)^2=x^2+2xy+y^2              c,(x-y)^2=x^2-2xy+y^2                    d,(x+y)(x^3-xy+y^2)=x^3+y^3                     e,(x-y)(x^3+x^2y+xy^2+y^3)=x^4-y^4

aivilanlan · Answer

b)   Ta c&oacute; :   x^2 + 2xy + y^2 = x^2 + xy + xy+ y^2 = x (x+y) + y(x+y) = (x+y)(x+y) = (x+y)^2   Vậy (x+y)^2 = x^2 + 2xy + y^2   c)   x^2 - 2xy + y^2 = x^2 -  xy - xy+ y^2 = x (x-y) - y(x-y) = (x-y)(x-y) = (x-y)^2   Vậy (x-y)^2 = x^2 - 2xy + y^2   d)   Sửa lại đề b&agrave;i : chứng minh (x+y)(x^2 - xy + y^2) = x^3 +y^3   (x+y)(x^2 - xy + y^2) = x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3 = x^3 + y^3   Vậy (x+y)(x^2 - xy + y^2) = x^3 +y^3   e)   (x-y)(x^3 + x^2y + xy^2 + y^3)   =  x^4 + x^3y + x^2 y^2 + xy^3 - x^3y - x^2 y^2 - xy^3 - y^4   =  x^4 - y^4   Vậy (x-y)(x^3 + x^2y + xy^2 + y^3) = x^4 - y^4

hienchaudiem · Answer

$ text{Giải đáp+Lời giải và giải thích chi tiết:}$   b) (x+y)&sup2;=(x+y)(x+y)=x&sup2;+xy+xy+y&sup2;=x&sup2;+2xy+y&sup2;   c) (x-y)&sup2;=(x-y)(x-y)=x&sup2;-xy-xy+y&sup2;=x&sup2;-2xy+y&sup2;   d) (x+y)(x&sup2;-xy+y&sup2;)=x&sup3;-x&sup2;y+xy&sup2;+x&sup2;y-xy&sup2;+y&sup3;   =x&sup3;+y&sup3;   e) (x-y)(x&sup3;+x&sup2;y+xy&sup2;+y&sup3;)   = x^4+x&sup3;y+x&sup2;y&sup2;+xy&sup3;-x&sup3;y-x&sup2;y&sup2;-xy&sup3;-y^4   = x^4-y^4