3. (A + B) · (A - B) = A2
- B2
(4p + 5q) · (4p - 5q) = (4p)2
- (5q)2
= 16p2
- 25q2
A B
A2
- B2
Azonosság:
Példa:
A B
49c2
- 36d2
= (7c + 6d) · (7c - 6d)
(A + B) · (A - B)
A B
(7c)2
- (6d)2
=
4. (A + B)3
= A3
+ 3A2
B + 3AB2
+ B3
(2c + 3d)3
= (2c)3
+ 3·(2c)2
·3d + (3d)3
=
= 8c3
+ 36c2
d + 54cd2
+ 27c3
A B
A3
+ 3A2
B +B3
Azonosság:
Példa:
+ 3AB2
+ 3·2c·(3d)2
5. (A - B)3
= A3
- 3A2
B + 3AB2
- B3
(3a - 2b)3
= (3a)3
- 3·(3a)2
·2b - (2b)3
=
= 27a3
- 54a2
b + 36ab2
- 8b3
A B
A3
- 3A2
B -B3
Azonosság:
Példa:
+ 3AB2
+ 3·3a·(2b)2
6. A3
- B3
= (A - B) · (A2
+ AB + B2
)
27x3
- 64y3
= (3x - 4y)
= (3x - 4y) · (9x2
+ 12xy + 16y2
)
A B
(A - B)
Azonosság:
Példa:
· (A2
+ AB + B2
)
· ((3x)2
+ 3x·4y + (4y)2
) =(3x)3
- (4y)3
=
7. A3
- B3
= (A - B) · (A2
+ AB + B2
)
27x3
- 64y3
= (3x - 4y)
= (3x - 4y) · (9x2
+ 12xy + 16y2
)
A B
(A - B)
Azonosság:
Példa:
· (A2
+ AB + B2
)
· ((3x)2
+ 3x·4y + (4y)2
) =(3x)3
- (4y)3
=