Use the Binomial Theorem to expand the expression $( x + 3 y ) ^ { 4 }$ .
A) $x ^ { 4 } + 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } + 108 x y ^ { 3 } + 81 y ^ { 4 }$
B) $x ^ { 4 } + 3 x ^ { 3 } y + 9 x ^ { 2 } y ^ { 2 } + 27 x y ^ { 3 } + 81 y ^ { 4 }$
C) $x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }$
D) $x ^ { 4 } + 81 y ^ { 4 }$
E) $x ^ { 4 } + 15 x ^ { 3 } y + 90 x ^ { 2 } y ^ { 2 } + 135 x y ^ { 3 } + 81 y ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion using the Binomial Theorem involves calculating the coefficients using the binomial coefficients formula, which for $(x + 3y)^4$ gives coefficients of 1, 4, 6, 4, 1, and multiplying these by the appropriate powers of 3y, resulting in the terms $x^4$, $12x^3y$, $54x^2y^2$, $108xy^3$, and $81y^4$.

Use the Binomial Theorem to Expand the Expression (x+3y)4( x + 3 y ) ^ { 4 }(x+3y)4

Use the Binomial Theorem to Expand the Expression $( x + 3 y ) ^ { 4 }$