## The Distributive Property

Given numbers *a, b*, and *c*, we are familiar since elementary grades that *a(b+c) = ab + ac*. This is what we call the *distributive property* of multiplication over addition. From commutative property, we also know that *xy = yx***; **therefore, *(b + c)a = a(b+c).*

Knowing this property, we can do a lot of mathematical operations. For example, we do not need to memorize FOIL (First-Outside-Inside-Last) , one of the rote strategies (no need to memorize) in multiplying binomials. That is, in *(a + b)(x + y), *we multiply *a(x + y), *multiply *b(x + y), *and then add both terms giving us *a(x + y) + b(x +y) *which is equal to *ax + ay + bx + by*. If we have solved this, we can definitely solve *(a + b)(x + y + z)* and also *(a + b + c)(x + y + z) *and multiplication of polynomials of many terms. » Read more