Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. In what situations would distribution become important?

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.