think of a condition under which product of anytwo binomials is a bionomial. you can support your answer with the help of one of the identies of factorization of polynomials
A binomial is a polynomial with two terms.
Try (x -a)(x + a)and see what you get.
To determine if the product of any two binomials could result in another binomial, we can consider the difference of squares identity for factoring polynomials.
The difference of squares identity states that for any two numbers a and b, the product (a^2 - b^2) can be factored as (a + b)(a - b).
Now, let's apply this identity to the product of two binomials: (x - a)(x + a).
Using the difference of squares identity, we can rewrite this expression as:
(x - a)(x + a) = (x)^2 - (a)^2 = x^2 - a^2.
So, when we multiply (x - a) and (x + a), we obtain the binomial x^2 - a^2, which consists of two terms and fits the definition of a binomial.
Therefore, the condition under which the product of any two binomials results in another binomial is when both binomials follow the pattern of the difference of squares identity.