Use the binomial theorem to expand the expression.
-$(x+y)^{4}$
A) $x^{4}+4 x^{3} y+6 x^{2} y^{2}+4 x y^{3}+y^{4}$
B) $x^{4}+4 x^{2} y^{2}+y^{4}$
C) $x^{4}+4 x^{3} y+4 x^{2} y^{2}+4 x y^{3}+y^{4}$
D) $x^{4}+4 x^{3}+6 x^{2}+4 x+1$

Question

Quizplus · Accepted Answer

The binomial theorem states that $(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k}y^k$. For $n=4$, the expansion is $x^{4}+4 x^{3} y+6 x^{2} y^{2}+4 x y^{3}+y^{4}$, matching choice A.

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

Use the Binomial Theorem to Expand the Expression $(x+y)^{4}$ A) $x^{4}+4 x^{3} y+6 x^{2} y^{2}+4 x y^{3}+y^{4}$