(2x-3y)^2(2x+3y)^2 (2x+y-1)(2x+y+1)
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(2x-3y)^2(2x+3y)^2 (2x+y-1)(2x+y+1)
(2x-3y)^2(2x+3y)^2
=[(2x-3y)(2x+3y)]^2
=(4x^2-9y^2)^2
(2x+y-1)(2x+y+1)
=(2x+y)^2-1
=4x^2+4xy+y^2-1
平方差公式[(2x-3y)*(2x+3y)]^2=[(2x)^2-(3y)^2]^2=(4x^2-9y^2)^2=16x^4-72x^2y^2+81y^4
(2x+y-1)(2x+y+1)=(2x+y)^2-1^2=4x^2+4xy+y^2-1
运用平方差公式
(2x-3y)^2(2x+3y)^2
=(2x-3y)(2x-3y)(2x+3y) (2x+3y)
=(2x-3y)(2x+3y)(2x-3y)(2x+3y)
=(4x^2-9y^2)(4x^2-9y^2)
=16x^4-72x^2y^2+81y^4
(2x+y-1)(2x+y+1)
=[(2x+y)-1][(2x+y)+1]
=(2x+y)^2-1
=4x^2+4xy+y^2-1
(2x-3y)^2(2x+3y)^2
=[(2x-3y)(2x+3y)]^2
=(4x^2-9y^2)^2
(2x+y-1)(2x+y+1)
=(2x+y)^2-1
=4x^2+4xy+y^2-1
这是一道化简题:解题步骤如下
(2x-3y)^2(2x+3y)^2 (2x+y-1)(2x+y+1)
=[(2x-3y)(2x+3y)]^2[(2x+y)-1][(2x+y)+1]
=(4x^2-9y^2)^2[(2x+y)^2-1]
主要考察平方差公式的熟练运用,平时多练习一下。
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