Rút gọn:
(a + b)^3 + (b + c)^3 + (c + a)^3 – 3(a + b)(b + c)(c + a)
Rút gọn: (a + b)^3 + (b + c)^3 + (c + a)^3 – 3(a + b)(b + c)(c + a)
By Everleigh
By Everleigh
Rút gọn:
(a + b)^3 + (b + c)^3 + (c + a)^3 – 3(a + b)(b + c)(c + a)
$(a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)$
`=a^3+3a^2b+3ab^2+b^3+b^3+3b^2c+3bc^2+c^3+c^3+3c^2a+3ca^2+a^3-6abc-3a^2b-3ac^2-3a^2c-3b^2c-3b^2a-3bc^2`
$=2a^3+2b^3+2c^3-6abc$
$(a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a) \\=a^3+3a^2b+3ab^2+b^3+b^3+3b^2c+3bc^2+c^3+c^3+3c^2a+3ca^2+a^3-6abc-3a^2b-3ac^2-3a^2c-3b^2c-3b^2a-3bc^2 \\=2a^3+2b^3+2c^3-6abc$