Question

factorise 16 x ⁴ - 72 x²y²+ 81 y⁴ plz find the answer ​

Answer 1

Answer:

The difference of squares identity can be written:

a

2

−

b

2

=

(

a

−

b

)

(

a

+

b

)

Hence we find:

16

x

4

−

81

y

4

=

(

4

x

2

)

2

−

(

9

y

2

)

2

16

x

4

−

81

y

4

=

(

4

x

2

−

9

y

2

)

(

4

x

2

+

9

y

2

)

16

x

4

−

81

y

4

=

(

(

2

x

)

2

−

(

3

y

)

2

)

(

4

x

2

+

9

y

2

)

16

x

4

−

81

y

4

=

(

2

x

−

3

y

)

(

2

x

+

3

y

)

(

4

x

2

+

9

y

2

)

The remaining quadratic factor has no linear factors with Real coefficients.

Answer 2

Explanation:

$(4 {x}^{2} {)}^{2} - 2(4 {x}^{2} )(9 {y}^{2} ) + (9 {y}^{2} {)}^{2}$

$= (4 {x}^{2} - 9 {y}^{2} {)}^{2}$

$( \: (2 {x}^{2} {)}^{2} - (3 {y}^{2} ) \: )$

$( \: (2 x + 3y) \: (2x - 3y) \: {)}^{2}$

so I hope it will help.