Question

Chứng minh các đẳng thức :

1) (a + b)^2= a^2 + 2ab + b^2

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

Answer 1

1) \(\left(a+b\right)^2\)

\(=\left(a+b\right)\left(a+b\right)\)

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

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

2) \(\left(a-b\right)^3\)

\(=\left(a-b\right)\left(a-b\right)\left(a-b\right)\)

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

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

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

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

Answer 2

`a)` 

`(a+b)^2`

`=(a+b)(a+b)`

`=a^2+ab+ab+b^2`

`=a^2+2ab+b^2`

`->` ĐPCM

`b)` `(a-b)^3`

`=(a-b)(a-b)(a-b)`

`=(a^2-2ab+b^2)(a-b)`

`=a^3-3a^2b+3ab^2-b^3`

`->` ĐPCM