Question

Factorise 8p^3+q^3 using identities

Answer 1

Step-by-step explanation:

Equation at the end of step 1 :

2kacubep3 + q3

Step 2 :

Trying to factor as a Sum of Cubes :

2.1 Factoring: 8p3+q3

Theory : A sum 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 : 8 is the cube of 2

Check : p3 is the cube of p1

Check : q3 is the cube of q1

Factorization is :

(2p + q) • (4p2 - 2pq + q2)

Trying to factor a multi variable polynomial :

2.2 Factoring 4p2 - 2pq + q2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

(2p + q) • (4p2 - 2pq + q2)

Answer 2

Answer:

(2p+q)(4p²-2pq+q²)

Step-by-step explanation:

To Factorise:-

8p³+q³

Formula Applied:-

a³+b³=(a+b)(a²-ab+b²)

Factorisation:-

(2p)³+(q)³

(2p+q)[(2p)²-(2p)(q)+(q)²]

(2p+q)(4p²-2pq+q²)