Question

计算：(u-v)^2-uv 1/4x^2-(1/2x-y)(1/2x+y) 因式分解：-10xy+25x^2+y^2 2)2x^2+5x-3 3)x^4

计算：(u-v)^2-uv 1/4x^2-(1/2x-y)(1/2x+y) 因式分解：-10xy+25x^2+y^2
2)2x^2+5x-3 3)x^4-6x^2+8 4)(x^2-y^2)-(x-y)^2 5)x^2n+2-4x^2x 6)(x^2+y^2)^2-4x^2y^2 7)(x+y)^2+2(x^2-y^2)+(x-y)^2 8)x^4-5x+4 9)x^3+2x^2-63x

Answer 1

计算：(u-v)^2-uv=u^2-3uv+v^2
1/4x^2-(1/2x-y)(1/2x+y)=1/4x^2-1/4x^2+y^2=y^2
因式分解：-10xy+25x^2+y^2=(5x-y)^2
2)2x^2+5x-3=(2x-1)(x+3)
3)x^4-6x^2+8=(x^2-2)(x^2-4)=(x^2-2)(x+2)(x-2)
4)(x^2-y^2)-(x-y)^2=(x+y)(x-y)-(x-y)^2=(x-y)(x+y-x+y)=2y(x-y)
5)x^2n+2-4x^2n=x^2n(x^2-4)=x^2n(x+2)(x-2)
6)(x^2+y^2)^2-4x^2y^2=(x^2+y^2+2xy)(x^2+y^2-2xy)=(x+y)^2(x-y)^2
7)(x+y)^2+2(x^2-y^2)+(x-y)^2 =(x+y)^2+2(x+y)(x-y)+(x-y)^2=(x+y+x-y)^2=4x^2
8)x^4-5x+4=x^4-x^2+x^2-5x-4=x^2(x+1)(x-1)+(x-4)(x-1)=(x-1)[x^3+x^2+x-4]
9)x^3+2x^2-63x=x(x^2+2x-63)=x(x-7)(x+9)

Answer 2

：(u-v)^2-uv =u^2-3vu+v^2
1/4x^2-(1/2x-y)(1/2x+y) =1/4x^2-(1/4x^2-y^2)
因式分解因为太多,就选几道解答吧
8) x^4-5x+4 =(x-4)(x-1)
9)x^3+2x^2-63x=x(x-7)(x+9)

Answer 3

计算：
(u-v)^2-uv=u^2-3uv+v^2
1/4x^2-(1/2x-y)(1/2x+y)=1/4x^2-1/4x^2+y^2=y^2
因式分解：
-10xy+25x^2+y^2=(5x-y)^2
2)2x^2+5x-3=(2x-1)(x+3)
3)x^4-6x^2+8=(x^2-2)(x^2-4)=(x^2-2)(x+2)(x-2)
4)(x^2-y^2)-(x-y)^2=(x+y)(x-y)-(x-y)^2=(x-y)(x+y-x+y)=2y(x-y)
5)x^2n+2-4x^2n=x^2n(x^2-4)=x^2n(x+2)(x-2)
6)(x^2+y^2)^2-4x^2y^2=(x^2+y^2+2xy)(x^2+y^2-2xy)=(x+y)^2(x-y)^2
7)(x+y)^2+2(x^2-y^2)+(x-y)^2 =(x+y)^2+2(x+y)(x-y)+(x-y)^2=(x+y+x-y)^2=4x^2
8)x^4-5x+4=x^4-x^2+x^2-5x-4=x^2(x+1)(x-1)+(x-4)(x-1)=(x-1)[x^3+x^2+x-4]
9)x^3+2x^2-63x=x(x^2+2x-63)=x(x-7)(x+9)