x 2 − 2 x y + y 2 − 25 = ( x − y ) 2 − 25 = = [( x − y ) − 5 ] [( x − y ) + 5 ] = = ( x − y − 5 ) ( x − y + 5 )
The expression x 2 − 25 − 2 x y + y 2 can be factored into ( x − y − 5 ) ( x − y + 5 ) by recognizing it as a difference of squares after factoring a perfect square from the first three terms. The factorization is completed using the property of difference of squares. Thus, the final answer is ( x − y − 5 ) ( x − y + 5 ) .
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[tex] \frac{1}{5} \times 30 \\ \\ = \frac{30}{5} = 6[/tex]