Question

1) triển khai các biểu thức sau theo hàng đẳng thức 

1) (x+1)²          2) (4+x)²         3) (6-x)²        4) (x-5)²

5) (5y+1)²             6) (2x+3)²            7) (2x-1)²           8) (3x-2)²

5) thu gọn về hàng đẳng thức 

1) 4x⁴ - 4x² +1          2) 4x² - 12x + 9            3) 36 + x² - 12x

4) 1-10x+25x²            5) x⁴ + 81 + 18x²         6) 4x² - 20 + 25

7) x² + 4y⁴ - 4xy²       8) x² + 10xy + +25y²     9) 9y² - 24xy + 16x²

 

Answer 1

Câu `1`

`1,(x+1)^2 = x^2 + 2  . x . 1 + 1^2 = x^2 + 2x + 1`

`2, (4 + x)^2=4^2 + 2 . 4 . x + x^2 = 16 + 8x+x^2`

`3, (6-x)^2 = 6^2 - 2 . 6 . x + x^2 = 36 - 12x + x^2`

`4, (x-5)^2  = x^2 - 2 . x . 5 + 5^2 = x^2 - 10x + 25`

`5, (5y+1)^2 = (5y)^2 + 2 . 5y . 1 + 1^2 = 25y^2 + 10y + 1`

`6,(2x+3)^2 = (2x)^2 + 2 . 2x . 3 + 3^2 = 4x^2 + 12x + 9`

`7, (2x-1)^2 = (2x)^2 - 2 . 2x . 1 + 1^2 = 4x^2 - 4x + 1`

`8, (3x-2)^2 = (3x)^2 - 2 . 3x . 2 + 2^2 = 9x^2 - 12x + 4`

Answer 2

Câu `5`

`1, 4x^4 - 4x^2 + 1= (2x^2)^2 - 2 . 2x^2 . 1 + 1^2= (2x^2 - 1)^2`

`2, 4x^2 - 12x + 9 = (2x)^2 - 2 . 2x . 3 + 3^2 = (2x-3)^2`

`3, 36 + x^2 - 12x = 36 - 12x + x^2  =6^2 - 2 . 6 . x  + x^2 = (6-x)^2`

`4, 1 - 10x + 25x^2 = 1^2 - 2 . 1 . 5x + (5x)^2 = (1-5x)^2`

`5, x^4 + 81 + 18x^2 = (x^2)^2 + 2 . x^2 . 9 + 9^2 = (x^2+9)^2`

`6, 4x^2 - 20x + 25 = (2x)^2 - 2 . 2x . 5 + 5^2 = (2x-5)^2`