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)
[tex]= (2t^x+r^y)(2t^x-r^y)\\= 4t^{2x}-2t^xr^y + 2t^xr^y - r^{2y}\\= 4t^{2x}-r^{2y}[/tex]
Compare [tex]4t^{2x}-r^{2y} \ with \ 4t^6-r^{10}[/tex]
[tex]4t^{2x} = 4t^6\\t^{2x} = t^6\\equate \ the \ powers\\2x = 6\\x = 3\\[/tex]
Get y;
[tex]r^{2y} = r^{10}\\2y = 10\\y = 5\\Hence \ x + y = 3+5 = 8[/tex]
Hence the sum of x and y is 8
