Question

Oblicz. 1/ ( x - 2 y )^2 =

2/ ( 2x + 3 y )^2 =

3/ ( pierw z 2 + pierw z 3 ) ^2 =

4/ ( pierw z 6 - 2 pierw z 3 )^2 =

Answer 1

1/  ( x - 2 y )^2 =  x^2 - 2*x*2y + (2y)^2= x^2 - 4xy + 4y^2= 4(1/4x^2 -xy +y^2)

2/  ( 2x + 3 y )^2 =(2x)^2+2*2x*3y+(3y)^2= 4x^2+12xy+9y^2= 

3/   ( pierw z 2 + pierw z 3 ) ^2 = (√2 + √3)^2=√2^2 + 2*√2*√3+ √3^2= 2 + 2*√6 + 3 =

= 5+2√6 

4/   ( pierw z 6 - 2 pierw z 3 )^2 =  (√6 -2√3)^2= √6^2 - 2*√6*2√3 + 2√3^2 =

= 6- 2*√6*√12 +12= 6- 2*√72 +12 = 6- 6√2 +12 =18-6√2 = 6(3-2√2)