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完全平方公式(a+b)~2=a~2+2ab+b~2与(a-b)~2=a~2-2ab+b~2相减,即刻得到一个公式:(a+b)~2-(ab)~2=4ab,并把它叫做和差积公式或和差积恒等式.它还可以写成(a+b)~2=(n-b)~2+4ab或(a+b)~2-4ab=(a-b)~2,下面举例说明它的应用.
(A + b) ~ 2 = a ~ 2 + 2ab + b ~ 2 and (ab) ~ 2 = a ~ 2-2ab + b ~ 2 are subtracted from the complete square equation (A + b) ~ 2 = (nb) ~ 2 + 4ab or (a + b) ~ 2 (ab) ~ 2 = 4ab and call it the sum of difference product and sum of difference products. 2-4ab = (ab) ~ 2, the following examples illustrate its application.