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$(4x^3y - 6x^2y^2 + 4xy^3 - y^4)$ can be expressed as: |
$(x - y)^4 - x^4$ $(x + y)^4 - y^4$ $x^4 - (x - y)^4$ $(x + y)^4 - x^4$ |
$x^4 - (x - y)^4$ |
(4x3y - 6x2y2 + 4xy3 - y4) = 2xy3 - 2x2y2 - y4 + 4x3y + 2xy3 - 4x2y2 = -y2 (-2xy + 2x2 + y2) + 2xy (2x2 + y2 - 2xy) = (2xy - y2) (2x2 + y2 - 2xy) = (x2 - x2 - y2 + 2xy) (x2 + x2 + y2 - 2xy) = [x2 - (x - y)2] [x2 + (x - y)2] = x4 - (x - y)4 |
