Question

solve the following problem?
​

Answer 1

Answer:

Step-by-step explanation:

9p+8q

Answer 2

Answer:

STEP

1

:

Equation at the end of step 1

(27 • (p3)) + 26q3

STEP

2

:

Equation at the end of step

2

:

33p3 + 26q3

STEP

3

:

Trying to factor as a Sum of Cubes

3.1 Factoring: 27p3+64q3

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 : 27 is the cube of 3

Check : 64 is the cube of 4

Check : p3 is the cube of p1

Check : q3 is the cube of q1

Factorization is :

(3p + 4q) • (9p2 - 12pq + 16q2)

Trying to factor a multi variable polynomial :

3.2 Factoring 9p2 - 12pq + 16q2

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

Factorization fails

Final result :

(3p + 4q) • (9p2 - 12pq + 16q2)