Question

What is the factored form of 8x^24-27y^6 someone please help me please

Answer 1

Answer:

x

24

−

27

y

6

Rewrite

8

x

24

as

(

2

x

8

)

3

.

(

2

x

8

)

3

−

27

y

6

Rewrite

27

y

6

as

(

3

y

2

)

3

.

(

2

x

8

)

3

−

(

3

y

2

)

3

Since both terms are perfect cubes, factor using the difference of cubes formula,

a

3

−

b

3

=

(

a

−

b

)

(

a

2

+

a

b

+

b

2

)

where

a

=

2

x

8

and

b

=

3

y

2

.

(

2

x

8

−

(

3

y

2

)

)

(

(

2

x

8

)

2

+

2

x

8

(

3

y

2

)

+

(

3

y

2

)

2

)

Simplify.

Tap for more steps...

(

2

x

8

−

3

y

2

)

(

4

x

16

+

6

x

8

y

2

+

9

y

4

)

x

24

−

27

y

6

Rewrite

8

x

24

as

(

2

x

8

)

3

.

(

2

x

8

)

3

−

27

y

6

Rewrite

27

y

6

as

(

3

y

2

)

3

.

(

2

x

8

)

3

−

(

3

y

2

)

3

Since both terms are perfect cubes, factor using the difference of cubes formula,

a

3

−

b

3

=

(

a

−

b

)

(

a

2

+

a

b

+

b

2

)

where

a

=

2

x

8

and

b

=

3

y

2

.

(

2

x

8

−

(

3

y

2

)

)

(

(

2

x

8

)

2

+

2

x

8

(

3

y

2

)

+

(

3

y

2

)

2

)

Simplify.

Tap for more steps...

(

2

x

8

−

3

y

2

)

(

4

x

16

+

6

x

8

y

2

+

9

y

4

)

Explanation: