计算(2a-3b)^2-(3a-2b)^2的正确结果是
2个回答

解法一

(2a-3b)^2-(3a-2b)^2

=[(2a-3b)+(3a-2b)][(2a-3b)-(3a-2b)]

=(2a-3b+3a-2b)(2a-3b-3a+2b)

=(5a-5b)(-a-b)

=5(a-b)(-a-b)

=5(b^2-a^2)

=5b^2-5a^2

解法二

(2a-3b)^2-(3a-2b)^2

=4a^2-12ab+9b^2-(9a^2-12ab+4b^2)

=4a^2-12ab+9b^2-9a^2+12ab-4b^2

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=-5a^2+5b^2