Define the operation by a b = (a+b)b. What is (3 5)-(5 3)?

2007 AMC 10B Problem 2

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Define the operation

\star

a\star b = (a+b)b.

What is

(3\star 5)-(5\star 3)?

-16

-8

0

8

16

Compute

3\star 5

and

5\star 3

separately

3\star 5=(3+5)\cdot 5

and

5\star 3=(5+3)\cdot 3

Since

3\star 5=(3+5)\cdot 5=40

and

5\star 3=(5+3)\cdot 3=24,

the difference is

40-24=16.

Thus, the correct answer is E.