Question 1175602
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Note: Use "^" to denote exponentiation -- e.g., "a^2" instead of just "a2".<br>
You are given the definition<br>
(2a+b)⊙(a+2b)=a^2+ab+b^2<br>
You are asked to evaluate 6⊙9.<br>
In this example, the operation is not defined in terms of numbers; it is defined in terms of algebraic expressions.  So you first need to find what the numbers a and b are.<br>
Being asked to evaluate 6⊙9, you know that (2a+b) is 6 and (a+2b) is 9.  So<br>
{{{2a+b=6}}}
{{{a+2b=9}}}<br>
One way to solve this particular pair of equations is to add the two equations:<br>
{{{3a+3b=15}}}
{{{a+b=5}}}<br>
Then that equation, together with the two original equations, quickly tells us a=1 and b=4.<br>
Now we can use those values to evaluate 6⊙9.<br>
6⊙9 = a^2+ab+b^2 = 1^1+1*4+4^2 = 1+4+16 = 21<br>