(a+b)

2

=a

2

+2ab+b

2

(a+b)

3

=a

3

+3a

2

b+3ab

2

+b

3

(a+b)

4

=a

4

+4a

3

b+6a

2

b

2

+4ab

2

+b

4

(a+b)

5

=a

5

+5a

4

b+10a

3

b

2

+10a

2

b

3

+5ab

4

+b

5

(a+b)

6

=a

6

+6a

5

b+15a

4

b

2

+20a

3

b

3

+15a

2

b

4

+6ab

5

+b

6

(a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ca

(a+b-c)

2

=a

2

+b

2

+c

2

+2ab-2bc-2ca

(a-b+c)

2

=a

2

+b

2

+c

2

-2ab-2bc+2ca

(a-b-c)

2

=a

2

+b

2

+c

2

-2ab+2bc-2ca

suma sześcianów: a

3

+ b

3

= (a+b)

.

(a

2

- ab + b

2

)

różnica sześcianów: a

3

- b

3

= (a - b)

.

(a

2

+ ab + b

2

)

(a-b)(a+b)=(a+b)(a

2

+ab+b

2

)(a+b)(a

2

+ab+b

2

)

(a-b)(a+b

2

)=a

2

-b

2

(a-b)(a

2

+ab+b

2

)=a

3

-b

3

(a+b)(a

2

-ab+b

2

)=a

3

+b

3

a

n-1

=(a-1)(a

n1

+a

n-2

+a

n-3

+…a

0

)

x

4

-1=(x-1)(x

3

+x

2

-

2

+x+1)

a

2

-144=(a+12)

2

=a

2

+2a12+144=a

2

+24a+144

(a-12)(a+12)