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Let's write them all out to see if we can find a pattern...

  row 1: 1 , ( a + b )^( 0 )  ...  row 2: 1  1 , ( a + b )^( 1 )  ...  row 3: 1  2  1 , ( a + b )^( 2 )  ...  row 4: 1  3  3  1 , ( a + b )^( 3 )  ...  row 5: 1  4  6  4  1 , ( a + b )^( 4 )  ...  row 6: 1  5  10  10  5  1 , ( a + b )^( 5 )  ...  row 7: 1  6  15  20  15  6  1 , ( a + b )^( 6 )
 

What's the trick?

What's the next line?

            1  ...  1  1  ...  1  2  1  ...  1  3  3  1  ...  1  4  6  4  1  ...  1  5  10  10  5  1  ...  1  6  15  20  15  6  1  ...  1  7  21  35  35  21  7  1  ...  This is called Pascal's Triangle.

Ones on the edge...  add the two guys above!

Whoa!
 

So, can you write out the expansion of( a + b )^( 7 )?