Question

fatorise 3y4 – 108y2​

Answer 1

Answer:

Note that both

27

y

3

=

(

3

y

)

3

and

64

=

4

3

are perfect cubes.

So it is natural to use the sum of cubes identity:

a

3

+

b

3

=

(

a

+

b

)

(

a

2

−

a

b

+

b

2

)

with

a

=

3

y

and

b

=

4

as follows:

27

y

3

+

64

=

(

3

y

)

3

+

4

3

=

(

3

y

+

4

)

(

(

3

y

)

2

−

(

3

y

)

(

4

)

+

4

2

)

=

(

3

y

+

4

)

(

9

y

2

−

12

y

+

16

)

Answer 2

Answer:

$3 {y}^{4} - 108 {y}^{2}$

$= 3 {y}^{2} ( {y}^{2} - 16 {y}^{2} )$

$= 3 {y}^{2} ( {y}^{2} - (4 {y})^{2}$

$= 3 {y}^{2} (y + 4y)(y - 4y)$