(1)99×101×9999 (2)(x-2y)(x+2y)-(x+2y)² (3)(2a+1)²-(1-2a)²
2个回答
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99×101×9999
=(100-1)(100+1)×9999
=9999²
=(10000-1)²
=100000000-20000-1
=99980001
(x-2y)(x+2y)-(x+2y)²
=x²-4y²-(x²+4xy+4y²)
=x²-4y²-x²-4xy-4y²
-8y²-4xy
(2a+1)²-(1-2a)²
=(2a+1-1+2a)(2a+1+1-2a)
=4a×2
=8a
(x+y)²-(x-y)²
(x+y-x+y)(x+y+x-y)
2y×2x
4xy
(a-b)²+a(2b-a)
=a²-2ab+b²+2ab-a²
=b²
=(100-1)(100+1)×9999
=9999²
=(10000-1)²
=100000000-20000-1
=99980001
(x-2y)(x+2y)-(x+2y)²
=x²-4y²-(x²+4xy+4y²)
=x²-4y²-x²-4xy-4y²
-8y²-4xy
(2a+1)²-(1-2a)²
=(2a+1-1+2a)(2a+1+1-2a)
=4a×2
=8a
(x+y)²-(x-y)²
(x+y-x+y)(x+y+x-y)
2y×2x
4xy
(a-b)²+a(2b-a)
=a²-2ab+b²+2ab-a²
=b²
来自:求助得到的回答
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(1)99×101×9999 =(100-1)×(100+1)×9999=9999×(10000-1)
=99990000-9999=99980001
(2)(x-2y)(x+2y)-(x+2y)² =x²-4y²-x²+4xy-4y²=-8y²+4xy=-4y(2y-x)
(3)(2a+1)²-(1-2a)²=(2a+1+1-2a)(2a+1-1+2a)=2×4a=8a
(4)(x+y)²-(x-y)² =(x+y+x-y)(x+y-x+y)=2x×2y=4xy
(5)(a-b)²+a(2b-a)=a²-2ab+b²+2ab-a²=b²
=99990000-9999=99980001
(2)(x-2y)(x+2y)-(x+2y)² =x²-4y²-x²+4xy-4y²=-8y²+4xy=-4y(2y-x)
(3)(2a+1)²-(1-2a)²=(2a+1+1-2a)(2a+1-1+2a)=2×4a=8a
(4)(x+y)²-(x-y)² =(x+y+x-y)(x+y-x+y)=2x×2y=4xy
(5)(a-b)²+a(2b-a)=a²-2ab+b²+2ab-a²=b²
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