大师作文网数学问题--------平方差公式&完全平方公式
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数学问题--------平方差公式&完全平方公式
1.把(x+2y-3)(x-2y-3)变为________,能应用平方差公式计算
2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
1.把(x+2y-3)(x-2y-3)变为________,能应用平方差公式计算
2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
(x+2y-3)(x-2y-3)=[(x-3)+2y]*[(x-3)-2y]
(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x^2-y^2)^2-(x^2-y^2)(x^2+y^2)
=(x^4-2x^2 *y^2+y^4)-(x^4-y^4)
=-2x^2*y^2+2y^4
再问： 2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²) =-(x-y)²(x-y)²-(x-y)(x+y)(x²+y²)① =-(x-y)^4-[(x²-y²)(x²+y²)]② =-（x-y)^4-[x^4-y^4]③ 对不对，如果对，怎么继续做，如果错了，哪里错了，第几步，请改正
再答： 第一步就已经错了 .(x+y)²(x-y)²-(x-y)(x+y）(x²+y²) =-(x-y)²(x-y)²-(x-y)(x+y)(x²+y²) 应该是： =[(x+y)(x-y)]²-(x-y)(x+y)(x²+y²)① =(x^2-y^2)^2-(x^2-y^2)(x^2+y^2) =(x^4-2x^2 *y^2+y^4)-(x^4-y^4) =-2x^2*y^2+2y^4
再问： -2x²y²+2y^4等不等于=-2(x-y)(x+y)y² 还有-2x²y²+2y^4一定对吗，我也求出是这个数
再答： 一定对 =-2x^2*y^2+2y^4 =-2(x^2-y^2)*y^2 =-2(x-y)(x+y)*y^2
(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x^2-y^2)^2-(x^2-y^2)(x^2+y^2)
=(x^4-2x^2 *y^2+y^4)-(x^4-y^4)
=-2x^2*y^2+2y^4
再问： 2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²) =-(x-y)²(x-y)²-(x-y)(x+y)(x²+y²)① =-(x-y)^4-[(x²-y²)(x²+y²)]② =-（x-y)^4-[x^4-y^4]③ 对不对，如果对，怎么继续做，如果错了，哪里错了，第几步，请改正
再答： 第一步就已经错了 .(x+y)²(x-y)²-(x-y)(x+y）(x²+y²) =-(x-y)²(x-y)²-(x-y)(x+y)(x²+y²) 应该是： =[(x+y)(x-y)]²-(x-y)(x+y)(x²+y²)① =(x^2-y^2)^2-(x^2-y^2)(x^2+y^2) =(x^4-2x^2 *y^2+y^4)-(x^4-y^4) =-2x^2*y^2+2y^4
再问： -2x²y²+2y^4等不等于=-2(x-y)(x+y)y² 还有-2x²y²+2y^4一定对吗，我也求出是这个数
再答： 一定对 =-2x^2*y^2+2y^4 =-2(x^2-y^2)*y^2 =-2(x-y)(x+y)*y^2