Factor by grouping to find a difference of squares

x^2 - y^2 - 2yz - z^2

Answer: (x+y+z)(x-y-z)

Hi,

x² - y² - 2yz - z² =

x² - (y² + 2yz + z²) =

x² - (y + z)² =

(x - (y + z))(x + (y + z)) =

(x - y - z)(x + y + z) <==ANSWER

I hope that helps!! :-)

x^2 - y^2 - 2yz - z^2

= x^2 - (y^2 + 2yz + z^2)

= x^2 - (y + z)^2 --------> difference of squares

= (x - (y+z)) (x + (y+z))

= (x - y - z) (x + y + z)


-- Ματπmφm --

x^2 - y^2 - 2yz - z^2 =
x^2-[y^2+2yz+z^2]=
x^2-(y+z)^2 ...........(this is a difference of squares)
=(x+y+z)(x-y-z)