When we multiply a monomial by a number, the number multiplies the numerical coefficient of the monomial.

Example

-8 × y = -8y, -1 × y = -y, 4 × -y = -4y, 4 × (-3xy) = -12xy

1. Compare the values of xy + xz and x(y + z)

(a) when x = 5, y = 6, z = 10

(b) when x = -25, y = 16, z = 8

2. Compare the values of xy - xy and x(y - z)

(a) when x = 12, y = 8, z = 3

(b) when x = 11, y = -8, z = -4

From your responses in Activity 2, you must have observed that the following properties of addition and multiplication.

Rule 2: For any three variables x, y and z the following rules hold.
1. Distributive property of multiplication over addition:
x(y + z) = xy + xz.
2. Distributive property of multiplication over subtraction:
x(y − z)= xy − xz.

The distributive property of multiplication over addition helps as to factor out common factors from the sum or difference of two algebraic expressions. This also helps us to sum up like terms.

For example,

4x + 5x = 4 × x + 5 × x = (4 + 5) × x = 9 × x = 9x.
3xy² + 6x²y = 3xy × y + 3xy × x = 3xy(y + x).

Addition of like terms is based on distributive property of multiplication over addition.