In two or more complete sentences, analyze how to find the third term in the expansion of (2x + y) 4.

The first term in the binomial is " x2 ", the second term in "3 ", and the power n is 6, so, counting from0 to 6, the Binomial Theorem gives me: (x2 + 3) 6 = 6C0 (x2) 6 (3) 0 + 6C1 (x2) 5 (3) 1 + 6C2 (x2) 4 (3) 2 + 6C3 (x2) 3 (3) 3 + 6C4 (x2) 2 (3) 4 + 6C5 (x2) 1 (3) 5 + 6C6 (x2) 0 (3) 6 Then simplifying gives me (1) (x12) (1) + (6) (x10) (3) + (15) (x8) (9) + (20) (x6) (27) + (15) (x4) (81) + (6) (x2) (243) + (1) (1) (729) = x12 + 18 x10 + 135 x8 + 540 x6 + 1215 x4 + 1458 x2 + 729