Question

Phân tích đa thức thành nhân tử

a.(x-y)^2-4

b.9-(x-y)^2

c.(x^2+4)^2-16x^2

Answer 1

a) (x-y)²-4=(x-y)²-2²=(x-y-2)(x-y+2)

b) 9-(x-y)²=3²-(x-y)²=(3-x+y)(3+x-y)

c) (x²+4)²-16x²=(x²+4)²-(4x)²=(x²+4-4x)(x²+4+4x)=(x-2)²(x+2)²

Answer 2

a) (x - y)² -  4

= (x - y)² -  2²

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

b) 9 - (x - y)²

= 3² - (x - y)²

= (3 - x + y)(3 + x - y)

c) (x² + 4)² - 16x²

= (x² + 4)² - (4x)²

= (x² + 4 - 4x)(x² + 4 + 4x)

= [(x + 2)(x - 2)]²

= (x² + 4)²

Answer 3

`a,`

`(x-y)^2 -4`

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

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

`b,`

`9 - (x-y)^2`

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

`= (3-x+y) (3 +x-y)`

`c,`

`(x^2 +4)^2 -16x^2`

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

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

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

`= (x-2)^2 (x+2)^2`

Answer 4

a, (x-y)^2-2^2
  =(x-y-2)(x-y+2)

b, =3^3-(x-y)^2 

    = (3-x+y)(3+x-y)

c,=(x^2+4)^2-(4x)^2

   = (x^2+4-4x)(x^2+4+4x)

Answer 5

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

b) \(9\) - \(\left(x-y\right)^2\)= \(3^2\)- \(\left(x-y\right)^2\)= \(\left(3-x-y\right)\left(3+x-y\right)\)

c) \(\left(x^2+4\right)^2-16x^2=\left(x^2+4\right)^2-\left(4x\right)^2=\left(x^2-4x+4\right)\left(x^2+4x+4\right)=\left(x-2\right)^2\left(x+2\right)^2=\left(x^2-4\right)^2\)