Solve {l}{25*13^{2}-15^{2}}{16*17^{2}-18^{2}}{9*21^2-13^2}{4*31^2-12^2}

$$\left. \begin{array} { l } { 25 \times 13 ^ { 2 } - 15 ^ { 2 } } \\ { 16 \times 17 ^ { 2 } - 18 ^ { 2 } } \\ { 9 \times 21 ^ { 2 } - 13 ^ { 2 } } \\ { 4 \times 31 ^ { 2 } - 12 ^ { 2 } } \end{array} \right.$$

Sort

$$3700,3800,4000,4300$$

Solution Steps

Calculate 13 to the power of 2 and get 169.

$$sort(25\times 169-15^{2},16\times 17^{2}-18^{2},9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Multiply 25 and 169 to get 4225.

$$sort(4225-15^{2},16\times 17^{2}-18^{2},9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Calculate 15 to the power of 2 and get 225.

$$sort(4225-225,16\times 17^{2}-18^{2},9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Subtract 225 from 4225 to get 4000.

$$sort(4000,16\times 17^{2}-18^{2},9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Calculate 17 to the power of 2 and get 289.

$$sort(4000,16\times 289-18^{2},9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Multiply 16 and 289 to get 4624.

$$sort(4000,4624-18^{2},9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Calculate 18 to the power of 2 and get 324.

$$sort(4000,4624-324,9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Subtract 324 from 4624 to get 4300.

$$sort(4000,4300,9\times 21^{2}-13^{2},4\times 31^{2}-12^{2})$$

Calculate 21 to the power of 2 and get 441.

$$sort(4000,4300,9\times 441-13^{2},4\times 31^{2}-12^{2})$$

Multiply 9 and 441 to get 3969.

$$sort(4000,4300,3969-13^{2},4\times 31^{2}-12^{2})$$

Calculate 13 to the power of 2 and get 169.

$$sort(4000,4300,3969-169,4\times 31^{2}-12^{2})$$

Subtract 169 from 3969 to get 3800.

$$sort(4000,4300,3800,4\times 31^{2}-12^{2})$$

Calculate 31 to the power of 2 and get 961.

$$sort(4000,4300,3800,4\times 961-12^{2})$$

Multiply 4 and 961 to get 3844.

$$sort(4000,4300,3800,3844-12^{2})$$

Calculate 12 to the power of 2 and get 144.

$$sort(4000,4300,3800,3844-144)$$

Subtract 144 from 3844 to get 3700.

$$sort(4000,4300,3800,3700)$$

To sort the list, start from a single element 4000.

$$4000$$

Insert 4300 to the appropriate location in the new list.

$$4000,4300$$

Insert 3800 to the appropriate location in the new list.

$$3800,4000,4300$$

Insert 3700 to the appropriate location in the new list.

$$3700,3800,4000,4300$$

Evaluate

$$4000,\ 4300,\ 3800,\ 3700$$