Question

(y-1)*(y-3)*(y-2)*(y-4)

Answer 1

$(y-1)(y-3)(y-2)(y-4)=(y^2-y-3y+3)(y^2-2y-4y+8)=\\=(y^2-4y+3)(y^2-6y+8)=\\=y^4-4y^3+3y^2-6y^3+24y^2-18y+8y^2-32y+24=\\=y^4-10y^3+35y^2-50y+24$

Answer 2

To simplify the expression (y-1)(y-3)(y-2)*(y-4), you can expand it and then combine like terms:

1. Expand the expression: (y-1)(y-3)(y-2)(y-4) = (y^2 - y - 3y + 3)(y^2 - 4y + 2)

2. Multiply the terms: (y^2 - y - 3y + 3)*(y^2 - 4y + 2) = y^4 - 4y^3 + 2y^2 - y^3 + 4y^2 - 2y - 3y^2 + 12y - 6

3. Combine like terms: y^4 - (4y^3 + y^3) + (2y^2 + 4y^2 - 3y^2) - (2y + 6) = y^4 - 5y^3 + 3y^2 - 2y - 6

So, the simplified expression is y^4 - 5y^3 + 3y^2 - 2y - 6.