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^4-6x^

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

(u-v)^2-uv
=u²-2uv+v²+uv
=u²-uv+v²

1/4x^2-(1/2x-y)(1/2x+y)
=1/4x²-1/4x²+y²
=y²
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^ +8=(x²-2)(x²-4)=(x-2)(x+2)(x²-2)
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(x²-4)=x^2n(x-2)(x+2)
6)(x^2+y^2)^2-4x^2y^2=x^4+2x²y²+y^4-4x²y²=(x²-y²)²=(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=(2x)²=4x²
8)x^4-5x^+4 =(x²-1)(x²-4)=(x-1)(x+1)(x-2)(x+2)
9)x^3+2x^2-63x=x(x²+2x-63)=x(x-7)(x+9)

Answer 2

buzhidao