lengte ⋅ breedte : 4 a ⋅ ( 3 a + 2 b ) hokjes tellen: 12 a 2 + 8 a b
4 a ⋅ ( 3 a + 2 b ) = 12 a 2 + 8 a b
12 ⋅ 50 2 + 8 ⋅ 50 ⋅ 80 = 12 ⋅ 2500 + 32000 = 62000
2 a ⋅ ( 5 a + 3 b ) = 10 a 2 + 6 a b
5 a ⋅ ( 2 a + 2 b ) = 10 a 2 + 10 a b
5 a ⋅ ( 3 a + 2 b ) = 15 a 2 + 10 a b .
a 2 ; a b ; a b ; b 2
De lengte is 3 a + 2 b . De breedte is 3 a + 4 b De oppervlakte van het plein is ( 3 a + 2 b ) ⋅ ( 3 a + 4 b ) .
9 a 2 ; 12 a b ; 6 a b ; 8 b 2 De oppervlakte van het plein is 9 a 2 + 18 a b + 8 b 2 .
( 3 a + 2 b ) ⋅ ( 3 a + 4 b ) = 9 a 2 + 18 a b + 8 b 2
lengte ⋅ breedte : ( 4 a + 3 b ) ⋅ ( 5 a + 4 b ) hokjes tellen: 20 a 2 + 31 a b + 12 b 2 Je vindt zo de gelijkheid: ( 4 a + 3 b ) ⋅ ( 5 a + 4 b ) = 20 a 2 + 31 a b + 12 b 2
a ⋅ ( 3 a + 4 b ) = 3 a 2 + 4 a b 6 a ⋅ ( 4 a + 3 b ) = 24 a 2 + 18 a b 5 a ⋅ ( 5 a + b ) = 25 a 2 + 5 a b
3 a 2 + 12 a b = 3 a ⋅ ( a + 4 b ) a 2 + 6 a b = a ⋅ ( a + 6 b ) 4 a 2 + 20 a b = 4 a ⋅ ( a + 5 b )
a ⋅ ( 3 a + 4 b ) = a ⋅ 3 a + a ⋅ 4 b = 3 a 2 + 4 a b 6 a ⋅ ( 4 a + 3 b ) = 6 a ⋅ 4 a + 6 a ⋅ 3 b = 24 a 2 + 18 a b 5 a ⋅ ( 5 a + b ) = 5 a ⋅ 5 a + 5 a ⋅ b = 25 a 2 + 5 a b
Ja.
a 2 + 4 a b + 3 b 2 = ( a + b ) ⋅ ( a + 3 b )
De gelijkheid is: 6 a 2 + 14 a b + 8 b 2 = ( 2 a + 2 b ) ⋅ ( 3 a + 4 b )