Bài 1: Khai triển các biểu thức sau dưới dạng tích của hai đa thức 1, x^2-81 2, 6-49x^2 3, 1/25 x^2-4 4,9/25x^2-1/25 5, 1x^2-9y^2 6,49y^2-25x^2 7,9/4x

1.

`x^2 – 81`

`=x^2 – 9^2`

`=(x – 9)(x + 9)`

2.

`64 – 49x^2`

`=8^2 – (7x)^2`

`=(8 – 7x)(8 + 7x)`

3.

`1/25x^2 – 4`

`=(1/5x)^2 – 2^2`

`=(1/5x – 2)(1/5x + 2)`

4.

`9/25x^2 – 1/25`

`=(3/5x)^2 – (1/5)^2`

`=(3/5x – 1/5)(3/5x + 1/5)`

5.

`1x^2 – 9y^2`

`=x^2 – (3y)^2`

`=(x – 3y)(x + 3y)`

6.

`49y^2 – 25x^2`

`=(7y)^2 – (5x)^2`

`=(7y – 5x)(7y + 5x)`

7.

`9/4x^2 – 16/25y^2`

`=(3/2x)^2 – (4/5y)^2`

`=(3/2x – 4/5y)(3/2x + 4/5y)`

8.

`16/25x^2 – 121/100y^2`

`=(4/5x)^2 – (11/10y)^2`

`=(4/5x – 11/10y)(4/5x + 11/10y)`

9.

`(1 + 2)^2 – 16`

`=(1 + 2)^2 – 4^2`

`=(1 + 2 – 4)(1 + 2 + 4)`

`=(3 – 4)(3 + 4)`

10.

`9 – (1/2x + 1)^2`

`=3^2 – (1/2x + 1)^2`

`=(3 – 1/2x – 1)(3 + 1/2x + 1)`

`=(2 – 1/2x)(4 + 1/2x)`

11.

`(6/5x^3)^2 – 49/25`

`=(6/5x^3)^2 – (7/5)^2`

`=(6/5x^3 – 7/5)(6/5x^3 + 7/5)`

12.

`x^2 – (2x + 1)^2`

`=(x – 2x – 1)(x + 2x + 1)`

`=(-x – 1)(3x + 1)`

13.

`4x^2 – 16(3x – 2)^2`

`=(2x)^2 – [4(3x – 2)]^2`

`=[2x – 4(3x – 2)][2x + 4(3x – 2)]`

`=(2x – 12x + 8)(2x + 12x – 8)`

`=(8 – 10x)(14x – 8)`

14.

`1/16y^2 – (1/2x – 1)^2`

`=(1/4y)^2 – (1/2x – 1)^2`

`=(1/4y – 1/2x + 1)(1/4y + 1/2x – 1)`

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