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The second volume of the eighth grade mathematics textbook (Beijing Normal University Edition) has an urgent answer!
5、25^7-5^ 12=(5^2)^7-5^ 12

=5^ 14-5^ 12

=5^ 12(5^2- 1)

=5^ 12×24

=5^ 1 1×5×24

=5^ 1 1× 120

So 25 7-5 12 can be divisible by 120.

6、( 1/2×x^2+xy+ 1/2×y^2)

=( 1/2)( x^2+2xy+y^2)

=( 1/2)(x+y)^2

=( 1/2) × 1^2

= 1/2

7、( 1)3^2004-3^2003=(3^2003)×(3- 1)=(3^2003)×2

(2)(-2)^ 10 1+(-2)^ 100=[(-2)^ 100]×[(-2)+ 1]

=[(-2)^ 100]×(- 1)=(2^ 100)×(- 1)=-2^ 100