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: 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 Log in to Reply

Answer:8Step-by-step explanation:Given the expression4t^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