Question

factorize 36/25x^4-y/16^4​

Answer 1

Answer: The answer is in the picture

Step-by-step explanation:

Answer 2

The factors of $\frac{36 {x}^{4} }{25} - \frac{ {y}^{4} }{16}$ are $\bf \red{ \left( { \frac{ \sqrt{6} {x}}{ \sqrt{5} } } - \frac{ {y}^{} }{2} \right ) \left( { \frac{ \sqrt{6} {x}}{ \sqrt{5} } } + \frac{ {y}^{} }{2} \right ) \left( { \frac{6 {x}^{2} }{5} } + \frac{ {y}^{2} }{4} \right )}$

Given:

• $\frac{36 {x}^{4} }{25} - \frac{ {y}^{4} }{16}$

To find:

• Find the factors of given polynomial.

Solution:

Identity to be used:

$\bf {a}^{2} - {b}^{2} = (a + b)(a - b)$

Step 1:

Convert the given expression as in LHS of identity.

$\frac{ {6}^{2} {( {x}^{2}) }^{2} }{ {5}^{2} } - \frac{ { {(y}^{2}) }^{2} }{ {4}^{2} }$

or

$\left( { \frac{6 {x}^{2} }{5} } \right) ^{2} - \left( { \frac{ {y}^{2} }{4} } \right) ^{2}$

here, it is clear that

$\bf a = \frac{6 {x}^{2} }{5}$

and

$\bf b = \frac{ {y}^{2} }{4}$

Step 2:

Apply identity to factorise.

$\frac{36 {x}^{4} }{25} - \frac{ {y}^{4} }{16} = \left( { \frac{6 {x}^{2} }{5} } - \frac{ {y}^{2} }{4} \right ) \left( { \frac{6 {x}^{2} }{5} } + \frac{ {y}^{2} }{4} \right )$

again the same identity can be applied in the first factor.

$\frac{36 {x}^{4} }{25} - \frac{ {y}^{4} }{16} = \left( { \frac{ \sqrt{6} {x}}{ \sqrt{5} } } - \frac{ {y}^{} }{2} \right ) \left( { \frac{ \sqrt{6} {x}}{ \sqrt{5} } } + \frac{ {y}^{} }{2} \right ) \left( { \frac{6 {x}^{2} }{5} } + \frac{ {y}^{2} }{4} \right )$

Thus,

The factors of expression are

$\bf \red{\frac{36 {x}^{4} }{25} - \frac{ {y}^{4} }{16} = \left( { \frac{ \sqrt{6} {x}}{ \sqrt{5} } } - \frac{ {y}^{} }{2} \right ) \left( { \frac{ \sqrt{6} {x}}{ \sqrt{5} } } + \frac{ {y}^{} }{2} \right ) \left( { \frac{6 {x}^{2} }{5} } + \frac{ {y}^{2} }{4} \right )}$

_______________________________

Learn more:

1) (3x-4y)^2-(2x-3y)^2 find factorise

https://brainly.in/question/2529352

2) 25(x+y)^2-36(x-2y)^2 factorise

https://brainly.in/question/3845215