Can a binomial be multiplied by a monomial such that the product is a monomial? If so, give an example.
No, it can't.
The product of monomial and binomial is a polynomial.
Example:
7 x ( x - 4 ) = 7 x ∙ x - 7 x ∙ 4 = 7x² - 28 x
Yes, a binomial can be multiplied by a monomial such that the product is a monomial. To do this, you simply multiply each term of the binomial by the monomial.
Let's take an example:
Consider the binomial (3x + 2) and the monomial 4x.
To get the product, we'll multiply each term of the binomial by the monomial:
(3x + 2) * 4x
First, we distribute the 4x to each term of the binomial:
(4x * 3x) + (4x * 2)
Then, we simplify each term:
12x^2 + 8x
As you can see, the result is a monomial, because it has only one term.
So, in this case, the product of the binomial (3x + 2) and the monomial 4x is the monomial 12x^2 + 8x.