Question

1. x² - 8x +16 - y²

2. 4x² - y² + 10y - 25

 

 

Answer 1

1.

\(\Leftrightarrow\left(x-4\right)^2-y^2\\ \Leftrightarrow\left(x-4-y\right)\left(x-4+y\right)\)

2.

\(\Leftrightarrow\left(2x\right)^2-\left(y^2-10y+25\right)\\ \Leftrightarrow\left(2x\right)^2-\left(y-5\right)^2\\ \Leftrightarrow\left(2x-y+5\right)\left(2x+y-5\right)\)

Answer 2

`1.`

`x^2 - 8x + 16-y^2`

`=x^2 - 2.4x+4^2 - y^2`

`=(x^2 - 2.4x+4^2) - y^2`

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

`=(x-4-y)(x-4+y)`

`2.`

`4x^2 - y^2 + 10y-25`

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

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

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

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

______________

Áp dụng HĐT: `A^2 - B^2 = (A-B)(A+B)`

Answer 3

`1)` `x^2 - 8x` `+ 16 - y^2`

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

`= (x` `- 4 - y``) (x -` `4 + y)`

`2)` `4x^2 - y^2` `+ 10y - 25`

`= 4x^2` `- (y^2 -` `10y + 25)`

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

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