Question

Suppose that when you factor 4t^6-r^10, you get (2t^x+r^y)(2t^x-r^y). determine the sum of t and r.

Answer 1

8

Explanation:

Given the expression

4t^6-r^10 we are to factorize in the form;

(2t^x+r^y)(2t^x-r^y)

First we need to factorize (2t^x+r^y)(2t^x-r^y)

`= (2t^x+r^y)(2t^x-r^y)\\= 4t^(2x)-2t^xr^y + 2t^xr^y - r^(2y)\\= 4t^(2x)-r^(2y)`

Compare
`4t^(2x)-r^(2y) \ with \ 4t^6-r^(10)`

`4t^(2x) = 4t^6\\t^(2x) = t^6\\equate \ the \ powers\\2x = 6\\x = 3\\`

Get y;

`r^(2y) = r^(10)\\2y = 10\\y = 5\\Hence \ x + y = 3+5 = 8`

Hence the sum of x and y is 8