( a + b ) ⋅ ( a + b ) = ( a + b ) 2 = a 2 + 2 a b + b 2 {\displaystyle (a+b)\cdot (a+b)=(a+b)^{2}=a^{2}+2ab+b^{2}}
Beispiel: ( 400 + 3 ) 2 = 160000 + 2400 + 9 = 162409 {\displaystyle (400+3)^{2}=160000+2400+9=162409}
( a − b ) ⋅ ( a − b ) = ( a − b ) 2 = a 2 − 2 a b + b 2 {\displaystyle (a-b)\cdot (a-b)=(a-b)^{2}=a^{2}-2ab+b^{2}}
Beispiel: ( 80 − 3 ) 2 = 6400 − 480 + 9 = 5929 {\displaystyle (80-3)^{2}=6400-480+9=5929}
( a + b ) ⋅ ( a − b ) = a 2 − b 2 {\displaystyle (a+b)\cdot (a-b)=a^{2}-b^{2}}
Beispiel: ( 4 s − 7 t ) ⋅ ( 4 s + 7 t ) = 16 s 2 − 49 t 2 {\displaystyle (4s-7t)\cdot (4s+7t)=16s^{2}-49t^{2}}
