Match each binomial expression with the set of coefficients of the terms obtained by expanding the expression. Note: Each set of coefficients is listed in the correct order.

(2x + y) 4

(x + 2y) 4

(x + 3y) 4

(3x + 2y) 4

Pairs

coefficients binomials

1, 12, 54, 108, 81

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81, 216, 216, 96, 16

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16, 32, 24, 8, 1

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1, 8, 24, 32, 16

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(2x + y) ^4 = (2x) ^4 + 4 (2x) ^3y + 6 (2x) ^2y^2 + 4 (2x) y^3 + y^4 = 16x^4 + 32x^3y + 24x^2y^2 + 8xy^3 + y^4 = > coefficients are 16, 32, 24, 8, 1

(x + 2y) ^4 = x^4 + 4x^3 (2y) + 6x^2 (2y) ^2 + 4x (2y) ^3 + (2y) ^4 = x^4 + 8x^3y + 24x^2y^2 + 32xy^3 + 16y^4 = > coefficients are 1, 8, 24, 32, 16

(x + 3y) ^4 = x^4 + 4x^3 (3y) + 6x^2 (3y) ^2 + 4x (3y) ^3 + (3y) ^4 = x^4 + 12x^3y + 54x^2y^2 + 108xy^3 + 81y^4 = > coefficient are 1, 12, 54, 108, 81