Đáp án `+` Giải thích các bước giải:

Bài `1`.

`1, 1/4 - x^2`

`=(1/2)^2 - x^2`

`=(1/2 -x)(1/2 + x)`

`2, 1-49x^2`

`=1^2 - (7x)^2`

`=(1-7x)(1+7x)`

`3, 4/9 x^2 - 16y^2`

`=(2/3 x)^2 - (4y)^2`

`=(2/3 x - 4y)(2/3 x + 4y)`

`4, (5/7 + x)^2`

`=(5/7)^2 + 2. 5/7 . x + x^2`

`=25/49 + 10/7x + x^2`

`5, (4x+3/5)^2`

`=(4x)^2 + 2 . 4x . 3/5 + (3/5)^2`

`=16x^2 + 24/5x + 9/25`

`6, (2/3x + 9y)^2`

`=(2/3x)^2 + 2 . 2/3 x . 9y + (9y)^2`

`=4/9 x^2 + 12xy + 81y^2`

`7, (y-1/3)^2`

`=y^2 - 2.y. 1/3 + (1/3)^2`

`=y^2 - 2/3y + 1/9`

`8, (3y-x)^2`

`=(3y)^2 - 2.3y.x + x^2`

`=9y^2 - 6xy + x^2`

`9, (7/2 x - 2/7y)^2`

`=(7/2x)^2 - 2. 7/2x . 2/7y + (2/7y)^2`

`=49/4 x^2 - 2xy + 4/49y^2`

Bài `2`.

`1, (4-x)(4+x)`

`=4^2 - x^2`

`=16-x^2`

`2, (8x+1)(1-8x)`

`=1^2 - (8x)^2`

`=1 - 64x^2`

`3, (1/2x - 5y)(5y + 1/2x)`

`=(1/2x)^2 - (5y)^2`

`=1/4x^2 - 25y^2`

`4, x^2 + 2/3 x + 1/9`

`=x^2 + 2 . x . 1/3 + (1/3)^2`

`=(x+1/3)^2`

`5, 4/9 y^2 + 25 + 20/3y`

`=(2/3y)^2 + 5^2 + 2 . 2/3y . 5`

`=(2/3y + 5)^2`

`6, 20xy+25y^2+4x^2`

`=2.5y.2x + (5y)^2 + (2x)^2`

`=(5y+2x)^2`

`7, -2x+1+x^2`

`=x^2-2x+1`

`=(x-1)^2`

`8, 4x^2 + 1/4 - 2x`

`=(2x)^2 + (1/2)^2 - 2 . 2x . 1/2`

`=(2x-1/2)^2`

`9, 16/9y^2 + 25/4x^2 - 20/3xy`

`=(4/3y)^2 + (5/2x)^2 - 2. 4/3y . 5/2x`

`=(4/3y - 5/2x)^2`