Question

1) a) (x+2y)²-(x-y)² b) (x+y)²-2 (x+y) +1 c) x²-4 d) 4y²-4

Answer 1

Formulele: ( x + y )² = x² + 2xy + y²
                  ( x - y )² = x² - 2xy + y²

a. ( x + 2y )² - ( x - y )² =
  = x² + 2*x*2y + 4y² - ( x² - 2xy + y² )
  = x² + 4xy + 4y² - x² + 2xy - y²
  = 3y² + 6xy 

b. ( x + y )² - 2( x + y ) + 1
 = x² + 2xy + y² - 2x - 2y + 1
 
c. x² - 4 = ( x - 4 )*( x + 4 ) ⇒ formula a² - b² = ( a - b)*( a + b )
 
d. 4y² - 4 = ( 2y - 2 )*( 2y + 2 ) ⇒ formula a² - b² = ( a - b)*( a + b )