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30 determine the coefficient on x 12 y 24 x12y24 in ( x 3 + 2 x y 2 + y + 3 ) 18 . (x3+2xy2+y+3)18. (be careful, as x x and y y now appear in multiple terms!)

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zubam2002

Answer: Coefficient of x²y² =5184

Step-by-step explanation:

18(3x + 4xy + y +3)*18(3x + 4xy + y + 3)

324( 9x² +12x²y + 3xy + 9x + 12x²y + 16x²y² + 4xy² +12xy + 3xy + 4xy² + y² + + 3y + 9x +12xy + 3y +9)

Already, x12y24x12y24 = 82944x²y²

From the expansion above, we have that: 324*16x²y²= 5184x²y²

Since, 82944x²y²/5184x²y² = 16

∴ Coefficient = 5184

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