Question

prove a cube + b cube =(a+b) (a square -ab + b square ​

Answer 1

Heya✌

Q u e s t i o n:

Prove-a³+b³=(a+b)(a²-ab+b²)

S o l u t i o n:

We know that,

(a+b)³=a³+b³+3ab(a+b)

So,

(a+b)³=a³+b³+3ab(a+b)

(a+b)³-3ab(a+b)=a³+b³

(a+b)³-3ab(a+b)=a³+b³

(a+b)(a+b)²-3ab(a+b)=a³+b³

(a+b)[(a+b)²-3ab]=a³+b³

(a+b)[a²+b²+2ab-3ab]=a³+b³

(a+b)(a²-ab+b²)=a³+b³

a³+b³=(a+b)(a²-ab+b²)

Hence, proved.