Задание 471

Решение:

• \({\largeа)}\ 86x-43y+2ax-ay=43(2x-y)+a(2x-y)=(2x-y)(43+a)\)

• \({\largeб)}\ 10by-25bx-6ay+15ax=5b(2y-5x)-3a(2y-5x)=(2y-5x)(5b-3a)\)

• \({\largeв)}\ x^2+xy-xz-yz=x(x+y)-z(x+y)=(x+y)(x-z)\)

• \({\largeг)}\ m^4+2-m-2m^3=m^4-m+2-2m^3=m(m^3-1)+2(1-m^3)=m(m^3-1)-2(m^3-1)=(m^3-1)(m-2)=(m-1)(m^2+m+1)(m-2)\)

• \({\largeд)}\ 5a^2-5ab+5b^2-5ab=5a(a-b)+5b(b-a)=5a(a-b)-5b(a-b)=(a-b)(5a-5b)=5(a-b)(a-b)=5(a-b)^2\)

• \({\largeе)}\ y-y^2-y^3+y^4=y(1-y)-y^3(1-y)=(1-y)(y-y^3)=y(1-y)(1-y^2)=y(1-y)(1-y)(1+y)=y(1-y)^2(1+y)\)

• \({\largeж)}\ b^3+b^2c-b^2d-bcd=b^2(b+c)-bd(b+c)=(b+c)(b^2-bd)=b(b+c)(b-d)\)

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