## 49. Trick

Maurice always disappointed his teachers, especially his math teachers. However, when he needed to calculate the square of 35, or 75, or finally 85, he always gave the correct answer in one second. The thing is, he had one trick up his sleeve that he was very proud of: to determine the square of any two-digit number ending in 5, he first multiplied the tens digit by the same number increased by 1, and then appended 25 to the number obtained. For example, when calculating \( (75)^2 \), he wrote " \( (7 \times 8) 25 \) " and easily got the desired result: 5625.

Please explain on what Maurice's trick is based?
49. Let $d$ be the number of tens in the number that needs to be squared. This means the last number has the form

$$
10 d+5 \text{. }
$$

Squaring it, we get

$$
100 d^{2}+100 d+25
$$

or

$$
100 d(d+1)+25
$$

For example,

$$
(85)^{2}="(8 \cdot 9) 25 "=7225
$$

Thus, Maurice's trick always gives the correct answer.