Toán Lớp 8: a(b+c)^2(b-c)+b(c+a)^2(c-a)+c(a+b)^2(a-b)

Question

Toán Lớp 8:  a(b+c)^2(b-c)+b(c+a)^2(c-a)+c(a+b)^2(a-b)

bichquyenlien · Answer

$a$ $(b+c)^{2}$ $(b-c)$$+b$$(c+a)^{2}$ $(c-a)$$+c$$(a+b)^{2}$ $(a-b)$   =$(ab-ac)$$(b^{2}$ $+2bc$$+c^{2} )$$+$$(bc-ab)$$(c^{2}$$+2ac $$+a^{2} )$$+$$(ac-bc)$$(a^{2}$ +$2ab$$+b^{2})$    =$ab^{3}$ +$2ab^{2}c$ $+abc^{2}$ $-ab^{2}c$ $-2abc^{2}$ $-ac^{3}$ $+bc^{3}$ $+2abc^{2}$ $+a^{2}bc$ $-abc^{2}$ $-2a^{2}bc$ $-a^{3}b$ $+a^{3}c$ $+2a^{2}bc$ $+ab^{2}c$ $-a^{2}bc$ $-2ab^{2}c$ $-b^{3}c$    =$ab^{3}$ $-ac^{3}$ $+bc^{3}$ $-a^{3}b$ $+a^{3}c$ $-b^{3}c$    #doaminhphuc2008      Ch&uacute;c bạn học tốt!        Bạn cho mik xin hay nhất cho nh&oacute;m nh&eacute;!

hoquyly · Answer

Giải đáp:       Lời giải và giải thích chi tiết:    a(b+c)^2(b-c)+b(c+a)^2(c-a)+c(a+b)^2(a-b)      =a    (    b    +    c    )    (        b^      2        &minus;        c    ^          2        )    +    b    (    c    +    a    )    (        c    ^          2        &minus;        a    ^          2        )    +    c    (    a    +    b    )    (        a    ^          2        &minus;        b    ^          2        )        =   (     a    b   +   a    c     )     (          b    ^         2      &minus;       c    ^         2         )    +   (     b    c   +   b    a     )     (          c    ^         2      &minus;       a    ^         2         )    +   (     c    a   +   c    b     )     (          a    ^         2      &minus;       b    ^         2         )              =   a        b           ^                3      &minus;   a    b        c           ^                2      +   a        b           ^                2       c   &minus;   a        c           ^                3      +   b        c           ^                3      &minus;       a           ^                2       b    c   +   a    b        c           ^                2      &minus;       a           ^                3       b   +       a           ^                3       c   &minus;   a        b           ^                2       c   +       a           ^                2       b    c   &minus;       b           ^                3       c                 =(b-a)(c-a)(c-b)(c+b+a)