Question

When Eric multiplied two binomials together, his result was a trinomial. An example is

(+2) G + 3) = x2 + 5x+6. Eric concluded that the product of any two binomials is a
trinomial. The product of which pair of binomials disproves Eric's conclusion?

Answer 1

(x + 4)(x - 4)

Explanation:

There are actually quite a lot of pairs of binomials the disproves Eric's conclusion, but they all model after the same special product: a^2 - b^2.

The special product a^2 - b^2 can be factored into (a + b)(a - b) and for all real a and b, it will come out as a binomial.

Here is an example:

(x + 4)(x - 4)

We can use the distributive property to get:

x^2 - 4x + 4x - 16

which is the same as

x^2 - 16

This would disprove Eric's conclusion.