Question

8x³-729y⁶. please answer it fast​

Answer 1

Answer:

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y6" was replaced by "y^6". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(8 • (x3)) - 36y6

STEP

2

:

Equation at the end of step

2

:

23x3 - 36y6

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: 8x3-729y6

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: 8x3-729y6

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 : 729 is the cube of 9

Check : x3 is the cube of x1

Check : y6 is the cube of y2

Factorization is :

(2x - 9y2) • (4x2 + 18xy2 + 81y4)

Trying to factor as a Difference of Squares:

3.3 Factoring: 2x - 9y2

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 4x2 + 18xy2 + 81y4

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

Factorization fails

Final result :

(2x - 9y2) • (4x2 + 18xy2 + 81y4

Answer 2

(2x)^3-(9y)^3
This is ur answer: