Let’s consider the given equation:

9 × (5 + 7) = (9 × 5) + (9 × 7)

Let’s solve both the sides of the equation.

9 × (5 + 7) = 9 x 12 = 108

(9 × 5) + (9 × 7) = 45 + 63 = 108

Notice that the product of a number and a sum is the same as multiplying each addend by the number and then adding the results.

According to distributive property of multiplication, multiplying a sum by any number is the same as multiplying each addend by the number separately and then adding the products.

a x (b + c) = ab + ac, where a, b, and c are any numbers (not equal to zero).

So, the distributive property of multiplication is used in the given equation.