Question

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)

Answer 1

(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

追问

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

追答

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

追问

-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

追答

一定对
=-2x^2*y^2+2y^4
=-2(x^2-y^2)*y^2
=-2(x-y)(x+y)*y^2

Answer 2

1.把(x+2y-3)(x-2y-3)变为[(x-3)+2y][(x-3)-2y]能应用平方差公式计算
2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x-y)(x+y)[(x+y)(x-y)-(x²+y²﹚]
=-2y²(x+y)(x-y)

追问

1.[x+（2y-3）][x-(2y+3)]行不行

追答

不行
必须是a+b,a-b的形式，你括号里不同

追问

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

Answer 3

你第二题的第一步就是错的。.(x+y)²(x-y)²和-(x-y)²(x-y)²是不相等的
正确做法就该是
.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x-y)(x+y)[(x+y)(x-y)-(x²+y²﹚]提取公因式(x-y)(x+y），再继续做
=-2y²(x+y)(x-y)

Answer 4

1.把(x+2y-3)(x-2y-3)变为(x+2y-3)(x-2y-3)=[(x-3)+2y]*[(x-3)-2y]能应用平方差公式计算

(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

追问

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

Answer 5

1.(x+2y-3)(x-2y-3)=(x-3)的二次方-4（y的二次方）=x的二次方-6x+9-4(y的二次方）
2.(x+y)的二次方*（x-y)的二次方-（x-y)(x+y)(x的二次方+y的二次方）=（x+y)（x-y)[(x+y)(x+y)-(x的二次方+y的二次方）]=(x的二次方-y的二次方）[(x+y)的二次方-(x的二次方+y的二次方）]=(x的二次方-y的二次方）(x的二次方+2xy+y的二次方-x的二次方-y的二次方）=（x的二次方-y的二次方）*2xy=2(x的三次方）y-2x(y的三次方）

Answer 6

1.原式=(x–3)^2-(2y)^2
2.原式=(x方-y方)^2–(x方-y方)(x方+y方)=2y^4-2x^2*y^2
希望可以帮到你，手机打的，有点简单，见谅