When we multiply a monomial and a monomial, we need not to use the distributive property; but we do use the property when dealing with the multiplication of monomial and binomial/trinomial/polynomial.

Example 1:

Monomial • monomial

(4x^3) • (3x^2)

= (4 • 3) • (x^3 • x^2)

= 12 • x5 = 12x5Notice, there isn't the application of law.

Example 2:

Monomial • binomial

x(x+4)

= x^2 + 4x

This problem requires the distributive property. You need to multiply each term in the parentheses by the monomial (distribute the x across the parentheses).

Example 3:

Monomial • trinomial

2x(x^2 +3x +4)

= 2x^3 + 6x^2 + 8x

Notice the distributive property at work again.

Example 4:

Monomial • polynomial

3x^2(x^3 -3x^2 +6x -5)

= 3x^5 - 9x^4 + 18x^3 - 15x^2

Again, the distributive property is needed along with the rule for multiplying powers.

Example 1:

Monomial • monomial

(4x^3) • (3x^2)

= (4 • 3) • (x^3 • x^2)

= 12 • x5 = 12x5Notice, there isn't the application of law.

Example 2:

Monomial • binomial

x(x+4)

= x^2 + 4x

This problem requires the distributive property. You need to multiply each term in the parentheses by the monomial (distribute the x across the parentheses).

Example 3:

Monomial • trinomial

2x(x^2 +3x +4)

= 2x^3 + 6x^2 + 8x

Notice the distributive property at work again.

Example 4:

Monomial • polynomial

3x^2(x^3 -3x^2 +6x -5)

= 3x^5 - 9x^4 + 18x^3 - 15x^2

Again, the distributive property is needed along with the rule for multiplying powers.