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. Continue reading