Задание 314

Решение:

• \({\largeа)}\ 2(x-1)+3(2-x)=\) \(2x\) \(-\) \(2\) \(+\) \(6\) \(-\) \(3x\) \(={-}x+4\)

• \({\largeб)}\ 2ab(3-2a)+4b(3a-7a^2)=\) \(6ab\) \(-\) \(4a^2b\) \(+\) \(12ab\) \(-\) \(28a^2b\) \(={-}32a^2b+18ab\)

• \({\largeв)}\ 7m(m-n)-3n(n+m)=7m^2\ -\) \(7mn\) \(-\ 3n^2\ -\) \(3mn\) \(=7m^2-10mn-3n^2\)

• \({\largeг)}\ (x-2y)\cdot2xy-28x^2y=\) \(2x^2y\) \(-\ 4xy^2\ -\) \(28x^2y\) \(={-}26x^2y-4xy^2\)

• \({\largeд)}\ x(x+2y)-y(2x-1)=x^2\ +\) \(2xy\) \(-\) \(2xy\) \(+\ y=x^2+y\)

• \({\largeе)}\ x(x-2y)-y(5-2x)=x^2\ -\) \(2xy\) \(-\ 5y\ +\) \(2xy\) \(=x^2-5y\)

• \({\largeж)}\ x^2(x+2y)-y(2x^2+1)=x^3\ +\) \(2x^2y\) \(-\) \(2x^2y\) \(-\ y=x^3-y\)

• \({\largeз)}\ x(x^2-y^2)+y(xy-y^2)=x^3\ -\) \(xy^2\) \(+\) \(xy^2\) \(-\ y^3=x^3-y^3\)

• \({\largeи)}\ (x-y)^2(x+1)-(x-y)^2x=(x-y)^2(x+1-x)=(x-y)^2\cdot1=(x-y)(x-y)=x^2\ -\) \(xy\) \(-\) \(xy\) \(+\ y^2=x^2-2xy+y^2\)

• \({\largeк)}\ (x+y)^2(x-1)-(x-y)^2x=(x+y)(x+y)(x-1)-(x-y)(x-y)x=(x^2+xy+xy+y^2)(x-1)-(x^2-xy-xy+y^2)x=(x^2+2xy+y^2)(x-1)-(x^2-2xy+y^2)x=\) \(x^3\) \(+\) \(2x^2y\) \(+\) \(xy^2\) \(-\ x^2-2xy-y^2-\) \(x^3\) \(+\) \(2x^2y\) \(-\) \(xy^2\) \(=4x^2y-x^2-2xy-y^2\)