5a-3(a-2)-2[a-3(3-2a)+6] a^nb^2[3b^n-1-2ab^n+1+(-1)^2003] (-
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5a-3(a-2)-2[a-3(3-2a)+6]

=5a-3a+6-2(a-9+6a+6)

=2a+6-2(7a-3)

=2a+6-14a+6

=-12a+12

a^nb^2[3b^n-1-2ab^n+1+(-1)^2003]

=a^n*b^2*[3b^(n-1)-2ab^(n+1)-1]

=3a^nb^(n+1)-2a^(n+1)b^(n+3)-a^nb^2

(-2x^2y^3)^3*(xy-3xy^2)

=-8x^6y^9*(xy-3xy^2)

=-8x^7y^10+24x^7y^11

5a(a-b+c)-2b(a+b-c)-4c(-a-b-c)

=5a^2-5ab+5ac-2ab-2b^2+2bc+4ac+4bc+4c^2

=5a62-2b^2+4c^2-7ab+9ac+6bc