Question

divide-
${x}^{4} - {y}^{4} by \: (x - y)$
please solve my problem​

Answer 1

Answer:

Given expression is x4y4−xy

We can take out xy as common.

Hence, the expression becomes:

xy(x3y3−1)

⇒xy[(xy)3−13]

We know that, a3−b3=(a−b)(a2+b2+ab)

Hence, the expression becomes:

xy[(xy−1)((xy)2+12+1(xy))]

⇒xy[(xy−1)(x2y2+1+xy)]

⇒xy(xy−1)(x2y2+xy+1)

Hence, x4y4−xy=xy(xy−1)(x2y2+xy+1).

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