Question

Solve the following question

Answer 1

Given:

The expressions are:

`(2a^2b)/(2c^2)\cdot (6ac^3)/(20b^4)`

`(x^2-y^2)/(4x+4y)\cdot (x+y)/(x-y)`

To find:

The simplified form of the given expressions.

Solution:

We have,

`(2a^2b)/(2c^2)\cdot (6ac^3)/(20b^4)`

It can be written as:

`(2a^2b)/(2c^2)\cdot (6ac^3)/(20b^4)=(12a^(2+1)bc^3)/(40b^4c^2)`

`(2a^2b)/(2c^2)\cdot (6ac^3)/(20b^4)=(3a^(3)c^(3-2))/(10b^(4-1))`

`(2a^2b)/(2c^2)\cdot (6ac^3)/(20b^4)=(3a^(3)c^(1))/(10b^3)`

Therefore, the value of the given expression is
`(3a^(3)c)/(10b^3)`.

We have,

`(x^2-y^2)/(4x+4y)\cdot (x+y)/(x-y)`

It can be written as:

`(x^2-y^2)/(4x+4y)\cdot (x+y)/(x-y)=((x+y)(x-y))/(4(x+y))\cdot (x+y)/(x-y)`

`(x^2-y^2)/(4x+4y)\cdot (x+y)/(x-y)=(x+y)/(4)`

Therefore, the value of the given expression is
`(x+y)/(4)`.