Asked by Kylie Naquin on Mar 10, 2024

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Verified

Use the Binomial Theorem to expand the expression (x+3y) 4( x + 3 y ) ^ { 4 }(x+3y) 4 .

A) x4+12x3y+54x2y2+108xy3+81y4x ^ { 4 } + 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } + 108 x y ^ { 3 } + 81 y ^ { 4 }x4+12x3y+54x2y2+108xy3+81y4
B) x4+3x3y+9x2y2+27xy3+81y4x ^ { 4 } + 3 x ^ { 3 } y + 9 x ^ { 2 } y ^ { 2 } + 27 x y ^ { 3 } + 81 y ^ { 4 }x4+3x3y+9x2y2+27xy3+81y4
C) x4+4x3y+6x2y2+4xy3+y4x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }x4+4x3y+6x2y2+4xy3+y4
D) x4+81y4x ^ { 4 } + 81 y ^ { 4 }x4+81y4
E) x4+15x3y+90x2y2+135xy3+81y4x ^ { 4 } + 15 x ^ { 3 } y + 90 x ^ { 2 } y ^ { 2 } + 135 x y ^ { 3 } + 81 y ^ { 4 }x4+15x3y+90x2y2+135xy3+81y4

Binomial Theorem

A principle in algebra that describes the algebraic expansion of powers of a binomial.

Expand

To express a mathematical expression in an extended form by removing parentheses or factoring, usually by applying the distributive property.

  • Utilize the binomial theorem and Pascal's triangle in addressing binomial expansion issues.
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Verified Answer

BC
Bryce Catherine

Mar 10, 2024

Final Answer :
A
Explanation :
The correct expansion using the Binomial Theorem involves calculating the coefficients using the binomial coefficients formula, which for (x+3y)4(x + 3y)^4(x+3y)4 gives coefficients of 1, 4, 6, 4, 1, and multiplying these by the appropriate powers of 3y, resulting in the terms x4x^4x4 , 12x3y12x^3y12x3y , 54x2y254x^2y^254x2y2 , 108xy3108xy^3108xy3 , and 81y481y^481y4 .