**Multiplying two digit numbers where the ten's digits are the
same and the sum of the unit's digits is 10**

What about 52 X 58 or 76 X 74?

You can do such calculations easily by remembering one simple rule.

In such cases you have to multiply the ten's digit number with one more than itself. It forms the first part of the answer. The second part of the answer can be got by multiplying the unit's digits.

Let's do it with an example:

43 X 47:

4 X 5 = 20 First part of the answer

3 X 7 = 21 Second part of the answer

The answer, therefore, is 2021.

You can try to understand the concept behind this.

Let ab and ac be two numbers satisfying the above criterion.

b + c = 10

ab X ac = (10a + b) X (10a + c) = 100a^2 + (10a (b + c)) + bc.

(We already know that (b + c) = 10.)

= 100a2 + 100a + bc = 100a(a + 1) + bc