Use Pascal s triangle to help expand the expression. $( x - y ) ^ { 4 }$
A) $x ^ { 4 } + 3 x ^ { 3 } y + 5 x ^ { 2 } y ^ { 2 } + 3 x y ^ { 3 } + y ^ { 4 }$
B) $x ^ { 4 } - 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } - 4 x y ^ { 3 } + y ^ { 4 }$
C) $x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }$
D) $x ^ { 4 } - 3 x ^ { 3 } y + 5 x ^ { 2 } y ^ { 2 } - 3 x y ^ { 3 } + y ^ { 4 }$
E) $x ^ { 4 } - 4 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } - 4 x y ^ { 3 } + y ^ { 4 }$

Question

Quizplus · Accepted Answer

The coefficients of the expansion of $(x - y)^4$ can be found in the 5th row of Pascal's triangle (1, 4, 6, 4, 1). The signs alternate starting with a positive for $x^4$, leading to the correct expansion: $x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4$.

Use Pascal S Triangle to Help Expand the Expression (x−y)4( x - y ) ^ { 4 }(x−y)4

Use Pascal S Triangle to Help Expand the Expression $( x - y ) ^ { 4 }$