\(\left(a-b\right)^2=\left(a-b\right)\left(a-b\right)=\left(a-b\right).a-\left(a-b\right).b=a^2-ab-\left(ab-b^2\right)=a^2-ab-ab+b^2=a^2-2.ab+b^2\)

\(\left(a-b\right)^3=\left(a-b\right)^2.\left(a-b\right)=\left(a^2-2.ab+b^2\right).\left(a-b\right)=\left(a^2-2ab+b^2\right).a-\left(a^2-2ab+b^2\right).b\)\(=\left(a^3-2.a^2.b+a.b^2\right)-\left(b.a^2-2.b^2.a+b^3\right)=a^3-2.a^2.b+a.b^2-b.a^2+2.b^2.a-b^3=a^3-3.a^2.b+3.b^2.a-b^3\)

a) \(\left(a+b\right).\left(a-b\right)=a.\left(a-b\right)+b.\left(a-b\right)=a^2-ab+ba-b^2\)\(=a^2-b^2\)

b) \(\left(a+b\right)^3=\left(a+b\right).\left(a+b\right).\left(a+b\right)=a.\left(a+b\right).\left(a+b\right)+b.\left(a+b\right).\left(a+b\right)\)

\(=\left(a^2+ab\right).\left(a+b\right)+\left(ba+b^2\right).\left(a+b\right)\)\(=a^2.\left(a+b\right)+ab.\left(a+b\right)+ba.\left(a+b\right)+b^2.\left(a+b\right)\)

\(=a^3+a^2b+a^2b+ab^2+ba^2+b^2a+b^2a+b^3\)\(=a^3+3a^2b+3ab^2+b^3\)

c) \(\left(a+b\right).\left(a^2-ab+b^2\right)=a.\left(a^2-ab+b^2\right)+b.\left(a^2-ab+b^2\right)\)

\(=a^3-a^2b+ab^2+ba^2-ab^2+b^3\)\(=a^3+b^3\)

d) \(\left(a-b\right).\left(a^2+ab+b^2\right)=a.\left(a^2+ab+b^2\right)-b.\left(a^2+ab+b^2\right)\)

\(=a^3+a^2b+ab^2-ba^2-ab^2-b^3\)\(=a^3-b^3\)

e) \(\left(a-b\right)^3=\left(a-b\right).\left(a-b\right).\left(a-b\right)=a.\left(a-b\right).\left(a-b\right)-b.\left(a-b\right).\left(a-b\right)\)

\(=\left(a^2-ab\right).\left(a-b\right)-\left(ba-b^2\right).\left(a-b\right)\)\(=a^2.\left(a-b\right)-ab.\left(a-b\right)-ba.\left(a-b\right)+b^2.\left(a-b\right)\)

\(=a^3-a^2b-a^2b+ab^2-ba^2+b^2a+b^2a-b^3\)

\(=a^3-3a^2b+3ab^2-b^3\)

1) (a+b).(a+b)=(a+b)2=a2+2ab+b2

2) (a-b)2=a2-2ab+b2

3) (a+b).(a-b)=a2-b2

4) (a+b)3=a3+3a2b+3ab2+b3

5) (a-b)3=a3-3a2b+3ab2-b3

6) (a+b).(a2-ab+b2)=a3+b3

7) (a-b).(a2+ab+b2)=a3-b3

a) ( a + b ) . ( a - b )

=a²-b²

b) ( a + b ) ³

=a³+3a²b+3ab²+b³

c) ( a + b ) . ( a² - ab + b² )

=a³+b³

d) ( a - b ) . ( a² + ab + b² )

=a³-b³

e) ( a - b )³

==a³-3a²b+3ab²-b³

Cái này lên lớp 8 mới hok nhưng bạn chịu khó hiểu nha :

 \(\left(a+b\right)\left(a^2-ab+b^2\right)\)

\(=a^3-a^2b+ab^2+a^2b-ab^2+b^3\)

Ta thấy dấu - vs dấu + triệt tiêu nha còn :

\(=a^3+b^3\)

Thế là xong 

Ủng hộ mik nha 

Thnaks

k còn cách khác s

1) (a+b).(a+b)=(a+b)²=a²+2ab+b²

2) (a-b)2=a²-2ab+b²

3) (a+b).(a-b)=a²-b²

4) (a+b)³=a³+3a²b+3ab²+b³

5) (a-b)³=a³-3a²b+3ab²-b³

6) (a+b).(a²-ab+b²)=a³⁺b³

7) (a-b).(a²+ab+b²)=a³-b³

mấy cái ày là hằng đẳng thức đáng nhớ mà

lấy a+a b+b

lấy b^2-a

lấy a.b b.a

a^3 +b

b^3-a

hai câu cuối thì mình k biết

1) \(\left(a+b\right).\left(a+b\right)=a.\left(a+b\right)+b.\left(a+b\right)=a^2+ab+b^2+ab\)

2) \(\left(a-b\right)^2=\left(a-b\right).\left(a-b\right)=a.\left(a-b\right)-b.\left(a-b\right)=a^2-ab-ab+b^2\)

\(=a^2+\left(-ab\right)+\left(-ab\right)+b^2\)

3) \(\left(a+b\right).\left(a-b\right)=a.\left(a-b\right)+b.\left(a-b\right)=a^2-ab+ab-b^2=a^2-b^2\)

\(=a^2+-\left(b^2\right)\)

4) \(\left(a+b\right)^3=\left(a+b\right).\left(a+b\right).\left(a+b\right)=a.\left(a+b\right).\left(a+b\right)+b.\left(a+b\right).\left(a+b\right)\)

\(=\left[a.\left(a+b\right)\right].\left(a+b\right)+\left[b.\left(a+b\right)\right].\left(a+b\right)=\left(a^2+ab\right).\left(a+b\right)+\left(ab+b^2\right).\left(a+b\right)\)

\(=a^2.\left(a+b\right)+ab.\left(a+b\right)+ab.\left(a+b\right)+b^2.\left(a+b\right)\)

\(=a^3+a^2b+a^2b+ab^2+a^2b+ab^2+b^2a+b^3\)

5) \(\left(a-b\right)^3=\left(a-b\right).\left(a-b\right).\left(a-b\right)=a.\left(a-b\right).\left(a-b\right)-b.\left(a-b\right).\left(a-b\right)\)

\(=\left(a^2-ab\right).\left(a-b\right)-\left(ba-b^2\right).\left(a-b\right)\)

\(=a^2.\left(a-b\right)-ab.\left(a-b\right)-ba.\left(a-b\right)+b^2.\left(a-b\right)\)

\(=a^3-a^2b-a^2b+ab^2-ba^2+b^2a-ba^2+b^2a-b^3\)

6) \(\left(a+b\right).\left(a^2-ab+b^2\right)=a.\left(a^2-ab+b^2\right)+b.\left(a^2-ab+b^2\right)\)

\(=a^3-a^2b+ab^2+ba^2-ab^2+b^3\)

\(=a^3+b^3\)

7) \(\left(a-b\right).\left(a^2+ab+b^2\right)=a.\left(a^2+ab+b^2\right)-b.\left(a^2+ab+b^2\right)\)

\(=a^3+a^2b+ab^2-ba^2-ab^2-b^3\)

\(=a^3-b^3\)

1 a^2+2ab+b^2

2 a^2-2ab+b^2

3 a^2-b^2

4 a^3+3a^2b+3ab^2+b^3

5 a^3-3a^2b+3ab^2-b^3

6 a^3+b^3

7 a^3-b^3

\(1)\left(a+b\right)\left(a+b\right)=\left(a+b\right)^2=a^2+2ab+b^2\)

\(2)\left(a-b\right)^2=a^2-2ab+b^2\)

\(3)\left(a+b\right)\left(a-b\right)=a^2-b^2\)

\(4)\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\)

\(5)\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\)

\(6)\left(a+b\right)\left(a^2-ab+b^2\right)=a^3+b^3\)

\(7)\left(a-b\right)\left(a^2+ab+b^2\right)=a^3-b^3\)

1)  (a+b)³=(a+b)(a+b)(a+b)=(a²+ab+ab+b²)(a+b)=(a²+2ab+b²​)(a+b)(a³+2a²b+ab²)+(a²b+2ab²+b³)=a³+2a²b+ab²+a²b+2ab²+b³

=a³+3a²b+3ab²+b³

bạn có thể giải tất cả hộ mình không ?

2)(a-b)³=(a-b)(a-b)(a-b)=(a²-ab-ab+b²)(a-b)=(a²-2ab+b²)(a-b)=(a³-2a²b+ab²)-(a²b-2ab²+b³)=a³-2a²b+ab²-a²b+2ab²-b³=a³-3a²b+3ab²-b³

3)   (a+b).(a²-ab+b²)=a³-a²b+ab²+a²b-ab²+b³=a³+b³

4)   (a-b).(a²+ab+b²)=(a³+a²b+ab²)-(a²b+ab²+b³)=a³+a²b+ab²-a²b-ab²-b³=a³-b³