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?
I wold say yes.
monomial is like kx^2
polynomial is like (ax^2 + bx + c)
kx^2 (ax^2+bx+c)
requires distributing the multiplication of kx^2 by each term of the polynomial.
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.
Distribution is a fundamental property in mathematics that allows us to multiply terms within parentheses by terms outside of parentheses. When dealing with expressions involving monomials (single terms) and polynomials (sums of terms), distribution is a common technique used to simplify and evaluate these expressions.
Yes, in most cases, we do use the property of distribution when multiplying monomials and polynomials. It allows us to expand an expression by distributing a multiplication or applying the multiplication property of exponents.
For example, let's consider the expression: 2x(3x + 4).
To simplify this expression, we can distribute the 2x to each term inside the parentheses:
2x * 3x + 2x * 4 = 6x^2 + 8x.
Without employing distribution, we would not be able to simplify this expression.
However, there are situations where distribution may not be necessary. For instance, if you're asked to find the product of two monomials, you can multiply their coefficients together and multiply their variables together using the exponent rules.
For example, given the monomials 5x^2 and 3x^3, you can directly multiply their coefficients as 5 * 3 = 15, and multiply their variables according to the exponent rule: x^2 * x^3 = x^(2+3) = x^5. So, the product of 5x^2 and 3x^3 is 15x^5.
In summary, distribution becomes important when dealing with expressions involving monomials and polynomials, as it allows us to simplify and evaluate these expressions by multiplying monomials with every term in the polynomial. However, in cases where we only have monomials, we can directly apply the multiplication property of exponents to find the product without using distribution.