Hướng dẫn trả lời:
Bài 1:
1) `(2x + 3)^3.`
`= (2x)^3 + 3.(2x)^2 .3 + 3.2x.3^2 + 3^3.`
`= 8x^3 + 36x^2 + 54x + 27.`
2) `(2y + 5/3)^3.`
`= (2y)^3 + 3.(2y)^2. 5/3 + 3.2y.(5/3)^2 + (5/3)^3.`
`= 8y^3 + 20y^2 + 50/3y + 125/27.`
3) `(x^2 + 2x)^3.`
`= (x^2)^3 + 3.(x^2)^2 .2x + 3.x^2.(2x)^2 + (2x)^3.`
`= x^6 + 6x^5 + 14x^2 + 8x^3.`
4) `(x^3+2/x)^3.`
`= (x^3)^3 + 3.(x^3)^2 . 2/x + 3.x^3.(2/x)^2 + (2/x)^3.`
`= x^9 + 6x^5 + 12x + 8/x^3.`
5) `(x^2y + 3/x)^3.`
`= (x^2y)^3 + 3.(x^2y)^2 . 3/x + 3.x^2y.(3/x)^2 + (3/x)^3.`
`= x^6y^3 + 9x^3y^2 + 27y + 27/x^3.`
Giải thích:
Áp dụng HĐT `(A + B)^3 = A^3 + 3A^2B + 3AB^2 + B^3.`
Bài 2:
1) `(2x - 1)^3.`
`= (2x)^3 - 3.(2x)^2. 1 + 3.2x.1^2 - 1^3.`
`= 8x^3 - 12x^2 + 6x - 1.`
2) `(2y - 5/3)^3.`
`= (2y)^3 - 3.(2y)^2 . 5/3 + 3.2y.(5/3)^2 - (5/3)^3.`
`= 8y^3 - 20y^2 + {50y}/3 - 125/27.`
3) `(ab^2 - 1)^3.`
`= (ab^2)^3 - 3.(ab^2)^2. 1 + 3.ab^2 . 1^2 - 1^3.`
`= a^3b^6 - 3a^2b^4 + 3ab^2 - 1.`
4) `(x^3 - 2/x)^3.`
`= (x^3)^3 - 3.(x^3)^2. 2/x + 3.x^3.(2/x)^2 - (2/x)^3.`
`= x^9 - 6x^5 + 12x - 8/x^3.`
5) `(xy^2 - 3/x)^3.`
`= (xy^2)^3 - 3.(xy^2)^2. 3/x + 3.xy^2.(3/x)^2 - (3/x)^3.`
`= x^3y^6 - 9xy^4 + {27y^2}/x - 27/x^3.`
Giải thích:
Áp dụng HĐT `(A-B)^3=A^3-3A^2 B+3AB^2-B^3.`
