Đáp án:
`(x+ 2y + 3z + t)^3 = x^3 + t^3 + 3xt^2 + 6yt^2 + 9zt^2 + 3tx^2 + 12xyt + 18xzt + 12ty^2 + 36yzt + 27z^2t + 6x^2y + 9x^2z + 12xy^2 + 36xyz + 27xz^2 + 8y^3 + 54yz^2 + 27z^3 + 36y^2z `
Giải thích các bước giải:
`(x+ 2y + 3z + t)^3`
` = [ (x+2y) + (3z + t)]^3`
` = (x+2y)^3 + 3 . (x+2y)^2 . (3z + t) + 3 . (x+2y) . (3z+t)^2 + (3z + t)^3`
` = [ x^3 + 3 . x^2 . 2y + 3 . x . (2y)^2 + (2y)^3] + 3 . (3z + t) . [ x^2 + 2 . x . 2y + (2y)^2] + (3x+ 6y) [ (3z)^2 + 2 . 3z . t + t^2] + [ (3z)^3 + 3 . (3z)^2 . t + 3 . 3z . t^2 + t^3]`
`= (x^3 + 6x^2y + 12xy^2 + 8y^3) + (9z + 3t)(x^2 + 4xy + 4y^2) + (3x + 6y)(9z^2 + 6zt + t^2) + (27z^3 + 27z^2t + 9zt^2 + t^3)`
` = (x^3 + 6x^2y + 12xy^2 + 8y^3)+ (9x^2z + 36xyz + 36y^2z + 3tx^2 + 12xyt + 12y^2t) + (27xz^2 + 18xzt + 3xt^2 + 54yz^2+ 36yzt + 6t^2y) + (27z^3 + 27z^2t + 9zt^2 + t^3)`
` = x^3 + 6x^2y + 12xy^2 + 8y^3 + 9x^2z + 36xyz + 36y^2z + 3tx^2 + 12xyt + 12y^2t + 27xz^2 + 18xzt + 3xt^2 + 54yz^2+ 36yzt + 6t^2y + 27z^3 + 27z^2t + 9zt^2 + t^3`
` = x^3 + t^3 + 3xt^2 + 6yt^2 + 9zt^2 + 3tx^2 + 12xyt + 18xzt + 12ty^2 + 36yzt + 27z^2t + 6x^2y + 9x^2z + 12xy^2 + 36xyz + 27xz^2 + 8y^3 + 54yz^2 + 27z^3 + 36y^2z `
