Question

Factorize 1) 16 a4 + 54 a
11

Answer 1

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "a4" was replaced by "a^4".

STEP

1

:

Equation at the end of step 1

24a4 + 54a

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

16a4 + 54a = 2a • (8a3 + 27)

Trying to factor as a Sum of Cubes:

3.2 Factoring: 8a3 + 27

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 : 27 is the cube of 3

Check : a3 is the cube of a1

Factorization is :

(2a + 3) • (4a2 - 6a + 9