Đáp án+Giải thích các bước giải:

Ví dụ `1`. 

`a)`

`(x + 1)² = x² + 2x + 1 `

`b) `

`(2x – 1)² = 4x² – 4x + 1 `

`c) `

`(x – 3)(3 + x) `

`= x(3 + x) – 3(3 + x)`

`= (3x + x²) – (9 + 3x) =`

`x² – 9 `

`d) `

`(x² + 2)² = x⁴ + 4x² + 4 `

Ví dụ `2`

`a)`

`(2x + 3y)² = 4x² + 12xy + 9y²`

`b) `

`(xy – 3)² = x²y² – 6xy + 9 `

`c)`

`(2xy – 1)(2xy + 1) = (2xy)² – 1² = 4x²y² – 1 `

`d)`

`(1/2 x² + y)(x² – 2y) `

`= 1/2 x²·x² – 1/2 x²·2y + y·x² – y·2y `

`= 1/2 x⁴ – x²y + x²y – 2y² `

`= 1/2 x⁴ – 2y² `

Ví dụ `4`.

`a) `

`(x + 3)³ `

`=x³ + 3x²·3 + 3x·3² + 3³ `

`= x³ + 9x² + 27x + 27 `

`b) `

`(x – 1/3)³ `

`= x³ – 3x²·(1/3) + 3x·(1/3)² – (1/3)³ `

`= x³ – x² + 1/3 x – 1/27 `

`c)`

`(x – 3y)³ `

`= x³ – 3x²·3y + 3x·(3y)² – (3y)³ `

`= x³ – 9x²y + 27xy² – 27y³ `

`d) `

`(x + (y²)/3)³ `

`= x³ + 3x²·((y²)/3) + 3x·((y²)/3)² + ((y²)/3)³ `

`= x³ + x²y² + ((y⁴)/3) + ((y⁶)/27)   `