Question

What types of polynomials do you think could factor using the relationship made

in the previous question?
If a is replaced with an x, and b is replaced with a 2, how would the equation
look, and what does it mean?
Create your own replacement of a and b and explain how your equations would
look and what would it mean?

Answer 1

The relationship in the previous question involves the difference of squares pattern, which applies to polynomials of the form:

a^2 - b^2

where a and b are any real numbers.

If we replace a with x and b with 2, the equation would look like:

x^2 - 2^2 = (x + 2)(x - 2)

This means that any polynomial of the form x^2 - 4 can be factored using the difference of squares pattern.

As for creating our own replacement of a and b, let's say we replace a with y and b with 3. Then the equation would look like:

y^2 - 3^2 = (y + 3)(y - 3)

This means that any polynomial of the form y^2 - 9 can be factored using the difference of squares pattern.