ແກ້ (r^30-1)div(r^10-1)

$$( r ^ { 30 } - 1 ) \div ( r ^ { 10 } - 1 )$$

ປະເມີນ

$$r^{20}+r^{10}+1$$

ຂັ້ນຕອນທາງອອກສັ້ນ

ປັດໃຈທີ່ນິພົດບໍ່ໄດ້ສ້າງເທື່ອ.

$$\frac{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)}{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)}$$

ຍົກເລີກ \left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right) ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)$$

ຂະຫຍາຍນິພົດ.

$$r^{20}+r^{10}+1$$

ຂະຫຍາຍ

$$r^{20}+r^{10}+1$$

ຂັ້ນຕອນທາງອອກສັ້ນ

ປັດໃຈທີ່ນິພົດບໍ່ໄດ້ສ້າງເທື່ອ.

$$\frac{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)}{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)}$$

ຍົກເລີກ \left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right) ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)$$

ຂະຫຍາຍນິພົດ.

$$r^{20}+r^{10}+1$$