Question

Which of the following polynomials is the expansion of (x - y)4? x4 - x3y + x2y2 - 2xy3 + y4 x4 -2x3y3 + y4 x4 - 2x3y + x 2y 2 - xy3 - y4 x4 - xy + y4

Answer 1

Answer:

$(x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4$.

Step-by-step explanation:

We want to find the polynomial that will result from expanding:

$(x-y)^4$.

Recall that we can use the Pascal's triangle to obtain the coefficient as:

1     4    6   4   1

Also note how the negative sign is going to alternate.

The power of x will decrease from left to right while the power of y increases from left to right

The expansion then becomes:

$(x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4$.