Question

How is the distributive property used when finding the product of two polynomials?

Answer 1

Duplicating Polynomials. To duplicate two polynomials, you apply the distributive property . Think about a straightforward model: duplicating a monomial 3x by the binomial x−2 . When you increase one binomial by another binomial, you need to utilize the distributive property over and again.

Answer 2

For this case we have that by definition, the distributive property establishes that:

$(a + b) (c + d) = ac + ad + bc + bd$

If we have two polynomials of the form:

$P (x) = ax ^ 2 + x\\G (x) = x + 3$

To multiply we apply the definition of distributive property, having that to multiply powers of the same base, the same base is placed and the exponents are added.

$P (x) * g (x) = (ax ^ 2 + x) (x + 3) = ax ^ 3 + 3ax ^ 2 + x ^ 2 + 3x$

Answer:

$(a + b) (c + d) = ac + ad + bc + bd$