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^2-16/25y^2
8,16/25x^2-121/100y^2
9, (1+2)^2-16
10,9-(1/2x+1)^2
11,(6/5x^3)^2-49/25
12,x^2-(2x+1)^2
13,4x^2-16(3x-2)^2
14,1/16y^2-(1/2x-1)^2
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)`