Question

Factorize each of the following expression:
x − y − x² + y²

Answer 1

\[x - y - x^2 + y^2 \]
\[ = (x - y) + ( y^2 - x^2 )\] [Regrouping the terms]
\[ = (x - y) + (y + x)(y - x)\]
\[ = (x - y) - (y + x)(x - y) [ \because (y - x) = - (x - y)]\]
\[ = (x - y)[1 - (y + x)]\]
\[ = (x - y)(1 - x - y)\]