What is the factored form of 8x^24 - 27y^6

### Answers

(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Step-by-step explanation:

4.722

Step-by-step explanation:

The required factored form of the given expression is

Step-by-step explanation: We are given to find the factored form of the following expression :

We will be using the following factorization formula :

So, the factorization of the given expression is as follows :

Thus, the required factored form of the given expression is

8x24-27y6 Final result : (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)
Step by step solution : Step 1 :Skip Ad

Equation at the end of step 1 : (8 • (x24)) - 33y6
Step 2 :Equation at the end of step 2 : 23x24 - 33y6
Step 3 :Trying to factor as a Difference of Squares :

3.1 Factoring: 8x24-27y6

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 8 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Trying to factor as a Difference of Cubes:

3.2 Factoring: 8x24-27y6

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 : 8 is the cube of 2

Check : 27 is the cube of 3

Check : x24 is the cube of x8

Check : y6 is the cube of y2

Factorization is :

(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Trying to factor as a Difference of Squares :

3.3 Factoring: 2x8 - 3y2

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Trying to factor a multi variable polynomial :

3.4 Factoring 4x16 + 6x8y2 + 9y4

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

Factorization fails

Final result : (2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Factoring:

Theory : A difference of two perfect cubes, can be factored into

Proof :

Check : 8 is the cube of 2

Check : 27 is the cube of 3

Check : is the cube of

Check : is the cube of

Factorization is :

(2x^8-3y^2)(4x^16+6x^8y^2+9y^4).