SOLUTION: I need help with the following: Multiply and then simplify completely: (3√7−5√5)(3√7+5√5) I have come up with several answer and I am having tro

Algebra ->  Equations -> SOLUTION: I need help with the following: Multiply and then simplify completely: (3√7−5√5)(3√7+5√5) I have come up with several answer and I am having tro      Log On


   

Question 1021526: I need help with the following:
Multiply and then simplify completely: (3√7−5√5)(3√7+5√5)
I have come up with several answer and I am having trouble showing my work
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply and then simplify completely:
%283sqrt%287%29-5sqrt%285%29%29%283sqrt%287%29%2B5sqrt%285%29%29
This FOILs as the difference of squares, the middle terms cancel so we have
9(7) - 25(5) = 63 - 125 = -62

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+=+3%2Asqrt%287%29+
Let +y+=+5%2Asqrt%285%29+
--------------------
+%28+3%2Asqrt%287+%29+-+5%2Asqrt%285%29%29%2A%28+3%2Asqrt%287+%29+%2B+5%2Asqrt%285%29+%29+
Make this substitution:
+x+-+y+%29%2A%28+x+%2B+y+%29+=+x%5E2+-+y%5E2+
---------------------------
+x%5E2+=+9%2A7+
+x%5E2+=+63+
and
+y%5E2+=+25%2A5+
+y%5E2+=+125+
----------------
+x%5E2+-+y%5E2+=+63+-+125+
+x%5E2+-+y%5E2+=+-62+
------------------
check answer:
I'll do it with calculator:

+sqrt%287%29+=+2.6458+
+sqrt%285%29+=+2.2361+
+%28+3%2A2.6458+-+5%2A2.2361+%29%2A%28+3%2A2.6458+%2B+5%2A2.2361+%29+=+-62+
+%28+7.9374+-+11.1805+%29%2A%28+7.9374+%2B+11.1805+%29+=+-62+
+%28+-3.2431%29%2A%28+19.1179+%29+=+-62+
+-62.0013+=+-62+
I assume the error is due to rounding off