Question

几道简单数学题

1.将1/4x+x³-x²因式分解的结果是
2.把多项式2mx²-4mxy+2my²因式分解的结果是
3.已知y=1/3x-1那么1/3x²-2xy+3y²-2的值是
4.当s=t+1/2时，代数式s²-2st+t²的值为

Answer 1

1.原式=x (x^2 -x +1/4) = x (x-1/2)^2
2.原式=2m(x^2-2xy+y^2) = 2m(x-y)^2
3.原式=(1/根号3 x-根号3 y)^2-2 把y=1/3x-1代入得 （根号3）-2
4.原式=(s-t)^2
由s=t+1/2得s-t=1/2 所以原式得1/4

Answer 2

1.原式=x(x²-x+1/4)=x(x-1/2)²
2.原式=2m(x²-2xy+y²)=2m(x-y)²
3.原式=1/3(x²-6xy+9y²)-2=1/3(x-3y)²-2
当y=1/3x-1时，原式=1/3(x-x+3)²-2=1
4.原式=(s-t)²
当s=t+1/2时，原式=(t+1/2-t)²=1/4

Answer 3

1、1/4x+x³-x²
=1/4x(4x²-4x+1)
=1/4x(2x-1)²
2、2mx²-4mxy+2my²
=2m(x²-2xy+2y²)
=2m(x-y)²
3、1/3x²-2xy+3y²-2
=1/3(x²-6xy+9y²)-2
=1/3(x-3y)²-2
=1/3[x-3*(1/3x-1)]²-2
=1/3(x-x+3)²-2
=3-2
=1
4、s²-2st+t²
=（s-t)²
=(t+1/2-t)²
=1/4

Answer 4

2. 2m乘以（x-y）的平方