分解因式:(x-a)^2-(x-b)^2=?;x+2x^2+x^3=?;5x^3-10x^2+5x=?已知x+y=1,求
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分解因式:(x-a)^2-(x-b)^2=?;x+2x^2+x^3=?;5x^3-10x^2+5x=?已知x+y=1,求1/2x^2+xy+1/2y^2的值全要过程
![分解因式:(x-a)^2-(x-b)^2=?;x+2x^2+x^3=?;5x^3-10x^2+5x=?已知x+y=1,求](/uploads/image/z/16717717-37-7.jpg?t=%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%EF%BC%9A%EF%BC%88x-a%29%5E2-%28x-b%29%5E2%3D%3F%3Bx%2B2x%5E2%2Bx%5E3%3D%3F%3B5x%5E3-10x%5E2%2B5x%3D%3F%E5%B7%B2%E7%9F%A5x%2By%3D1%2C%E6%B1%82)
(x-a)^2-(x-b)^2
=(x-a+x-b)^2(x-a-x+b)^2
=(2x-a-b)^2(-a+b)^2
x+2x^2+x^3
=x(1+2x+x^2)
=x(x+1)^2
5x^3-10x^2+5x
=5x(x^2-2x+1)
=5x(x-1)^2
1/2x^2+xy+1/2y^2
=1/2(x^2+2xy+y^2)
=1/2(x+y)^2
=1/2(1)^2
=1/2
=(x-a+x-b)^2(x-a-x+b)^2
=(2x-a-b)^2(-a+b)^2
x+2x^2+x^3
=x(1+2x+x^2)
=x(x+1)^2
5x^3-10x^2+5x
=5x(x^2-2x+1)
=5x(x-1)^2
1/2x^2+xy+1/2y^2
=1/2(x^2+2xy+y^2)
=1/2(x+y)^2
=1/2(1)^2
=1/2
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