i am not understanding what is distributive property

Let us consider two whole numbers 4 and 5. The product of 4 and 5 is 20.

Now, if we break 5 as (2 + 3), then we can write 4 × 5 as 4 × (2 + 3) = 20

Observe that (4 × 2) + (4 × 3) = 8 + 12 = 20

Thus, 4 × (2 + 3) = (4 × 2) + (4 × 3)

This is called the distributive property of whole numbers for multiplication over addition. We can generalize this property as follows.

“**Suppose we have three whole numbers ****a****, ****b****, and ****c****. It does not matter whether we add ****b**** and ****c**** first, and then multiply the product with ****a**** or whether we multiply ****a**** with ****b**** and ****a**** with ****c**** and then add the two products”.**

**This can be written as**

**a ****× (****b ****+**** c****)**** = a ****×**** b ****+**** a ****×**** c**

**This property also holds for multiplication over subtraction i.e.,**

**a ****× (****b ****–**** c****)**** = a ****×**** b ****–**** a ****×**** c**

This property can be very useful in multiplying bigger numbers. Suppose we have to multiply 19 and 45. It would take us a long time to do this if we follow the usual approach.