Question

the factorization of 27a3 +8 is​

Answer 1

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "a3" was replaced by "a^3".

STEP

1

:

Equation at the end of step 1

33a3 - 8

STEP

2

:

Trying to factor as a Difference of Cubes

2.1 Factoring: 27a3-8

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 : 27 is the cube of 3

Check : 8 is the cube of 2

Check : a3 is the cube of a1

Factorization is :

(3a - 2) • (9a2 + 6a + 4)

Trying to factor by splitting the middle term

2.2 Factoring 9a2 + 6a + 4

The first term is, 9a2 its coefficient is 9 .

The middle term is, +6a its coefficient is 6 .

The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 9 • 4 = 36

Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 6 .

-36 + -1 = -37

-18 + -2 = -20

-12 + -3 = -15

-9 + -4 = -13

-6 + -6 = -12

-4 + -9 = -13

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

(3a - 2) • (9a2 + 6a + 4)