We Distribute, Yet Things Multiply

The fundamental property a(b+c) = ab

The fundamental property a(b+c) = ab + ac, which allows us to distribute multiplication over addition. This property works with any numbers including

When we increase or decrease numbers

When we increase or decrease numbers in a product, we can predict the change using algebra. For example, if both numbers a and b are increased by 1, t

The identity (a+m)(b+n) = ab +

The identity (a+m)(b+n) = ab + an + bm + mn shows how products change when numbers are modified by any amounts m and n. The increase is an + bm + mn.

Using distributive property to multiply quickly

Using distributive property to multiply quickly with numbers like 11, 101, 1001, etc. For example, 3874 × 11 = 3874 × (10+1) = 38740 + 3874 = 42614.

(a+b)² = a² + 2ab +

(a+b)² = a² + 2ab + b². This identity can be visualized geometrically as a square with side length (a+b) divided into four parts: two squares of areas