Question

Resolve 27a³ + 8b³ into two real factors​

Answer 1

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b3" was replaced by "b^3". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(27 • (a3)) + 23b3

STEP

2

:

Equation at the end of step

2

:

33a3 + 23b3

STEP

3

:

Trying to factor as a Sum of Cubes:

3.1 Factoring: 27a3+8b3

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 : 8 is the cube of 2

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :

(3a + 2b) • (9a2 - 6ab + 4b2)

Trying to factor a multi variable polynomial :

3.2 Factoring 9a2 - 6ab + 4b2

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

Factorization fails

Final result :

(3a + 2b) • (9a2 - 6ab + 4b2)

Answer 2

27a³+8b³

(3a+2b).(9a²-6ab+4b²)

here is your answer

can you become my friend

mark me as brainlist

# ItzYourQueen01