a, Ta có:

(x+y)² - y² 

= x² + 2xy + y² - y²

= x² + 2xy

= x(x+2y)              (đpcm)

b, Ta có: (x² + y²) - (2xy)² 

= (x² - 2xy + y²)(x² + 2xy + y²)

= (x-y)²(x+y)²       (đpcm)

c, Ta có: (x-y)²-(x+y)²

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

= 2x . (-2y)

= -4xy           (đpcm)

Đáp án:

$\text{ a) (x+y)² - y² = x(x+2y) }$

$\text{⇔ (x+y-y)(x+y+y) = x(x+2y) }$

$\text{⇔ x(x+2y) = x(x+2y) }$ 

$\text{Vậy (x+y)² - y² = x(x+2y) }$

$\text{b) (x²+y²)² - (2xy)² = (x+y)² . (x-y)² }$

$\text{⇔ (x²+y² + 2xy) .(x²+ y² -2xy) = (x+y)² .(x-y)² }$

$\text{⇔ (x+y)² .(x-y)² = (x+y)² .(x-y)² }$

$\text{Vậy (x² + y²)² - (2xy)² = (x+y)² .(x-y)² }$

$\text{c) (x-y)² - (x+y)² = -4xy }$

$\text{⇔ (x-y +x+y) . (x-y-x-y) = -4xy }$

$\text{⇔ 2x . (-2y) = -4xy }$

$\text{⇔ -4xy = -4xy }$

$\text{Vậy (x-y)² - (x+y)² = -4xy  }$