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

Answer:

8

Step-by-step 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