Question

factorise
(1) P^3-343
(2)a^9-b^9
Please write in full explanation

Answer 1

(1)Theory: A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check:  343  is the cube of   7  

Check:  p3 is the cube of   p1

Factorization is :

            (p - 7)  •  (p2 + 7p + 49)

For (2) refer the attachment below

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