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